LIBRARY 

UNIVERSITY  OF 

CALIFORNIA 

IRVINE 


LB 
113/ 


PRIVATE  LIBRARY  OF 
L.  H.  PETERSON, 

NO. 


A  Comparative  Study  of  Achievement 
in  Country  and  Town  Schools 

By  Norman  Frost,  Ph.D. 


TEACHERS  COLLEGE,  COLUMBIA  UNIVERSITY 
CONTRIBUTIONS  TO  EDUCATION,  NO.  Ill 


Published  by 

Teathers  (SnllEgt,  Qlnlnmbta  ^ntnersttg 

New  York  City 

1921 


Copyright,  1921,  by  Norman  Frost 


M  QUIDDY    PRINTING   CO. 
NASHVILLE 


ACKNOWLEDGMENTS 

THIS  study  has  been  made  possible  by  the  help  of  a  number  of  peo- 
ple. Thanks  are  extended  to  the  school  officials  who  have  fur- 
nished data  or  permitted  tests  to  be  given  in  the  schools  in  their  charge. 
Indebtedness  is  acknowledged  to  the  many  members  of  the  faculty  of 
Teachers  College,  Columbia  University,  who  have  assisted  by  con- 
structive criticism.  Special  thanks  are  due  Dr.  N.  L.  Engelhardt,  Dr. 
G.  D.  Strayer  and  Dr.  E.  L.  Thorndike  for  advice,  suggestion  and 
encouragement. 

N.  F. 


CONTENTS 

I.     Previous   Objective    Studies    of    Achievement    in    Country 

Schools    .     i 7 

II.     Purpose  and  Scope  of  the  Present  Study 15 

III.  Achievement  Measured  by  the  Trabue  Language  Scales     .     18 

IV.  Achievement  Measured  by  the  Courtis  Standard  Research 

Tests  in  Arithmetic  Series  B 33 

V.     Achievement  Measured  by  the  Thorndike   Silent  Reading 

Scale  Alpha  2 56 

VI.     Summary  and  Conclusions .     61 

Appendix 68 


A  COMPARATIVE  STUDY  OF  ACHIEVEMENT 
IN  COUNTRY  AND  TOWN  SCHOOLS 

CHAPTER  I 

PREVIOUS  OBJECTIVE  STUDIES  OF  ACHIEVEMENT  IN 
COUNTRY  SCHOOLS 

An  accurate  comparison  of  school  systems  in  objective  terms  is 
necessary  for  the  proper  solution  of  problems  in  regard  to  the  organi- 
zation and  administration  of  schools.  Such  a  comparison  is  made 
possible  by  the  use  of  standardized  tests  in  the  systems  to  be  compared, 
and  has  been  made  with  great  profit  in  many  city  school  systems.  To 
a  much  more  limited  extent  the  same  kind  of  comparisons  have  been 
made  among  rural  schools. 

The  Ohio  Surrey  Commission  Report,  1914,  on  pages  133  and  134, 
reports  the  median  score  on  the  Hillegas  scale  of  97  eighth  grade 
composition  papers  from  Delaware  (city)  as  521.6,  and  the  sim- 
ilar median  of  118  eighth  grade  composition  papers  from  Dela- 
ware (county)  is  reported  as  387.6.  On  pages  135j^.  of  the  same 
report  results  of  handwriting  scores  by  the  Ayres  Scale  are  given. 
These  results  are  from  1,397  pupils  in  176  rural  schools  in  21  coun- 
ties in  Ohio ;  from  214  pupils  in  the  three  upper  grades  of  the  rural 
schools  of  Delaware  County ;  from  312  pupils  in  the  three  upper  grades 
in  the  city  schools  of  Delaware ;  and  from  a  small  city  in  Iowa,  based  on 
results  obtained  by  L  King  and  H.  Johnson,  whose  study  was  originally 
published  in  the  Journal  of  Educational  Psychology  (III:  514-520). 
Tables  are  given  which  show,  among  other  things,  that  in  the  small 
Iowa  city  98  per  cent  of  the  eighth  grade  papers  were  scored  over  50 
on  the  Ayres  Scale ;  that  77.8  per  cent  of  the  like  papers  from  the  Ohio 
rural  schools  made  like  scores  ;  73.5  per  cent  from  the  Delaware  County 
(rural)  ;  and  91.3  per  cent  from  the  city  of  Delaware.  In  conclusion 
it  is  stated  that  "the  handwriting  in  both  Delaware  city  and  Iowa  city 
is  on  the  whole  better  than  in  the  rural  schools  .  .  ."  and  that 
"there  is  greater  uniformity  in  the  city  schools." 

Results  of  work  with  the  Courtis  Standard  Research  Tests  in 
Arithmetic  Series  B  and  Starch's  Arithmetical  Scale  A  are  reported 
on  pages  33^.  of  A  Study  of  Rural  Schools  in  Travis  County,  Bul- 
letin of  the  University  of  Texas,  December,  1916.  Tables  are  given 
showing  grade  results  of  the  Courtis  tests,  and  the  discussion  is  sum- 

7 


8  Study  of  Achievement  in  Country  and  Town  Schools 

marized  in  this  statement :  "In  every  instance  the  number  of  examples 
attempted  and  the  number  of  examples  worked  correctly  were  lower 
in  this  group  of  country  schools  than  for  the  corresponding  grades  in 
Boston  and  Detroit,  and  among  the  11,800  pupils  tested  in  Iowa. 
Sometimes  this  difference  was  as  great  as  50  per  cent,  the  average  dif- 
ference being  approximately  25.5  per  cent."  Concerning  the  results  of 
the  Starch  test  the  following  statement  is  made:  "As  a  test  for  the 
reasoning  ability  of  these  pupils  on  arithmetical  problems.  Starch's 
Arithmetical  Scale  A  was  used.  The  results  from  the  fourth  to  the 
eighth  grade  were  duly  tabulated.  Each  grade  scored  below  the  scale 
standard  established  for  it.  The  fourth  grade  was  11  per  cent  below 
standard ;  the  fifth  grade  19  per  cent ;  the  sixth  grade  5  per  cent ;  the 
seveinth  grade  6  per  cent ;  and  the  eighth  grade  8  per  cent." 

In  1916  the  State  Board  of  Education  in  Connecticut  made  a  num- 
ber of  studies  of  the  schools  in  certain  of  the  towns  (townships)  of 
that  state.  The  tests  used  were  not  standardized,  but  they  were  uni- 
form for  all  of  these  investigations.  The  subjects  covered  were  arith- 
metic, reading,  language,  history,  geography  and  spelling.  Compara- 
tive tables  for  different  towns  in  the  state  are  given  in  these  reports, 
which  were  published  separately  as  bulletins  of  the  Connecticut  State 
Board  of  Education.  The  following  quotations  give  an  idea  of  the 
character  of  the  findings :  "The  accomplishment  of  the  pupils  as  shown 
by  the  tests  given  is  only  from  fair  to  poor.  Especially  is  this  true 
in  view  of  the  retardation  in  the  schools."  {Educational  Enquiry, 
Trumbull,  p.  29.)  "While  the  results  in  this  fundamental  test  are  not 
satisfactory,  they  nevertheless  compare  favorably  with  the  work  of 
pupils  in  the  towns  of  Seymour,  Westbrook  and  Bloomfield."  {Edu- 
cational Enquiry,  New  Hartford,  p.  24.)  "It  would  appear  from  the 
above  that  the  children  cannot  add  with  facility  and  accuracy,  although 
some  progress  is  being  made  from  grade  to  grade,"  {Educational 
Enquiry,  Seymour,  p.  23.)  "It  is  obvious  that  most  pupils  in  these 
towns  are  unable  to  interpret  and  solve  correctly  simple  problems." 
{Educational  Enquiry,  Westbrook,  p.  25.) 

In  an  unpublished  survey  of  the  Haldane  school.  Cold  Springs,  N.  Y., 
made  in  1917,  a  table  on  page  30  gives  a  comparison  of  median  achieve- 
ments in  English  composition  by  grades  (Hillegas  Scale,  Nassau 
County  Extension),  which  includes  grade  medians  for  the  schools  of 
Mobile  County,  Ala.,  and  for  the  city  of  Mobile.  In  every  grade  re- 
ported the  median  for  the  city  schools  is  higher  than  that  for  the 
country  schools. 


Previous  Objective  Studies  9 

The  Survey  and  Report  of  The  Virginia  Public  Schools  Education 
Commission,  published  in  1919,  gives  comparative  results  for  country 
and  city  schools  for  the  following  tests :  Thorndike  Reading  Scale  A2, 
Virginia  Reading  Test  Sigma  8,  Virginia  General  Examination  Exer- 
cise 1,  Ayres  Spelling  Scale,  Starch  Scale  for  Measuring  Handwriting, 
Woody  Arithmetic  Scale  Series  B,  Courtis  Standard  Research  Test 
in  Arithmetic  Series  B,  and  the  Nassau  County  Supplement  to  the 
Hillegas  Scale  for  Measuring  English  Composition.  About  sixteen 
thousand  different  children  were  examined  with  from  six  to  forty  dif- 
ferent tests.  Of  these  sixteen  thousand  children  about  five  thousand 
were  in  grades  three  to  seven  of  rural  white  schools.  The  general 
character  of  the  results  is  indicated  by  the  following  quotations  from 
the  report :  *Tn  summary  it  may  be  said  that  the  condition  of  reading 
in  the  Virginia  city  schools  is  fairly  satisfactory.  Such  deficiencies 
as  do  exist  will  be  easily  adjusted  when  once  attention  is  called  to  them. 
In  the  rural  schools,  however,  there  is  a  deficiency  that  should  be  met 
by  vigorous  remedial  measures."  (p.  121.)  In  regard  to  handwriting 
the  report  has  this  to  say :  "The  scores  for  rural  schools  having  four 
or  more  rooms  compare  favorably  with  those  for  city  schools,  and  the 
progress  is  regular  from  grade  to  grade.  The  average  progress  is 
four-tenths  of  a  scale  step  per  year,  which  is  less  than  it  should  be  by 
Starch  Standards.  The  one-room  country  school  shows  the  poorest 
record."  (p.  122.)  In  regard  to  spelling  it  says:  "The  most  notable 
deficiencies  are  in  the  one-room  school  (all  grades)  and  in  the  seventh 
grade  for  every  group  tested.  In  three  cases  the  deficiency  is  a  year 
or  more  of  progress  as  measured  on  the  Ayres  Scale."  (p.  123.) 
Concerning  arithmetic  the  report  states  that  "The  average  seventh 
grade  score  for  Virginia  city  children  at  the  end  of  the  year  is  15.9, 
which  is  the  sixth  grade  Woody  Standard  for  the  beginning  of  the 
year,  and  it.  is  15.1,  or  less  than  the  sixth  grade  Woody  Standard  for 
the  seventh  grade  in  the  best  graded  rural  schools.  For  the  one-room 
rural  schools  it  is  only  13.5."  (p.  124.)  "What  is  true  of  addition 
is  generally  true  of  the  results  in  subtraction,  multiplication  and  divi- 
sion." (p.  125.)  In  general  conclusion  in  regard  to  the  results  in 
rural  schools  the  report  says :  "The  inferiority  of  the  small  rural  school 
is  apparent  from  the  figures  given.  In  reality  that  inferiority  is  even 
greater  since  in  all  non-city  schools  children  are  on  the  average  about 
a  year  older  than  city  children  and  in  the  one-room  schools  children 
are  on  the  average  about  a  year  and  a  half  older  than  city  children  in 
each  of  the  upper  grades  of  the  elementary  schools.     In  arithmetic  the 


10  Study  of  Achievement  in  Country  and  Town  Schools 

inferiority  of  the  one-room  school  is  perhaps  most  marked,  children 
in  such  schools  being  on  the  average  one  grade  behind  children  in  the 
larger  non-city  schools."     (p.  129.) 

E.  H.  Taylor,  in  an  article,  "A  Comparison  of  the  Arithmetical 
Abilities  of  Rural  and  City  School  Children,"  published  in  the  Journal 
of  Educational  Psychology  (V:  461-466,  October,  1914),  reports  the 
results  of  Courtis  arithmetic  tests  given  by  himself  and  the  county 
superintendent  to  most  of  the  children  in  a  county  in  Illinois.  Tests 
were  given  to  309  children  in  28  schools.  Results  are  tabulated  and 
compared  by  grades  with  scores  of  7,008  children,  published  by  Courtis 
in  Elementary  School  Teacher  (XII:  133/).  The  comparison  shows 
that  the  rural  schools  are  consistently  below  the  others ;  grades  3  and 
4  of  the  rural  schools  are  approximately  a  grade  below,  grades  5  and  6 
are  almost  two  grades  below,  grade  7  is  more  than  one  grade  but  less 
than  two  grades  below,  and  grade  8  is  at  least  two  grades  below. 

Richard  Zeidler  reports  in  Elementary  School  Journal  (XVI :  542- 
555)  tests  of  efficiency  in  the  rural  and  village  schools  of  Santa 
Clara  County,  California.  Courtis  arithmetic  tests  were  given  by  the 
writer  to  587  children  in  grades  5  to  8  inclusive.  Results  are  compared 
with  a  group  of  20  small  Western  cities,  with  Salt  Lake  City,  and  with 
Butte.  The  writer  concludes  that  "From  these  tables  it  will  be  noted 
that  rural  and  village  schools  in  Santa  Clara  County,  in  every  subject 
and  in  every  grade,  fall  below  the  median  scores  for  the  cities.  This 
inferiority  ranges  as  high  as  600  per  cent,  as  is  shown  in  division  in 
the  fifth  grade  of  Santa  Clara  County  compared  with  the  fifth  grade 
division  in  Salt  Lake  City,  Utah.  It  must  be  admitted,  however,  that 
Salt  Lake  City  has  an  enviable  record."  ".  .  .  It  will  be  seen  that 
rural  and  village  schools  of  Santa  Clara  County  fall,  on  the  average, 
fully  two  grades  below  Salt  Lake  City,  and  one  grade  below  the  twenty 
small  cities." 

The  same  author  reports  tests  in  silent  reading  in  the  rural 
schools  of  Santa  Clara  County,  California,  in  Elementary  School 
Journal  (XVII:  55-62).  Starch  Reading  Tests  were  given  by  the 
writer  in  26  rural  schools.  Eight  of  these  schools  were  one-teacher 
schools,  7  were  two-teacher,  7  were  three-teacher,  and  4  had  more 
than  three  teachers.  The  results  are  tabulated  in  detail,  and  compared 
with  results  from  San  Jose.  Mr.  Zeidler  says :  "In  comparing  the 
median  number  of  words  read  per  second  in  the  rural  schools  with 
the  medians  for  the  San  Jose  schools,  it  will  be  seen  that  the  rural 
schools  compare  very  favorably  with  the  city  schools.     The  fifth  grade 


Previous  Objective  Studies  11 

falls  2/10  below,  while  the  seventh  and  eighth  grades  score  higher 
than  the  city  schools  of  that  community.  But  if  we  make  a  compari- 
son of  both  the  rural  schools  of  Santa  Clara  County  and  the  city 
schools  of  San  Jose  with  the  standardized  scores,  we  find  that  both  fall 
below,  with  the  single  exception  of  the  seventh  grade  in  the  rural 
schools,  which  surpasses  the  standards  by  1/10."  "In  the  reproduction 
of  the  thought,  the  rural  school  children  fall  below  the  children  of  the 
city  of  San  Jose.  There  is  a  marked  diflcerence  in  the  third  grade, 
where  the  median  for  the  rural  schools  is  7.5  as  against  12.5  in  the 
city." 

Charles  L.  Harlan  is  the  author  of  "A  Comparison  of  the  Writing, 
Spelling  and  Arithmetic  Abilities  of  Country  and  City  Children,"  pub- 
lished in  Educational  Administration  and  Supervision  (II:  560-573). 
Tests  were  given  to  359  pupils  in  21  rural  schools  in  a  "typical"  county 
in  Pennsylvania.  Handwriting  was  scored  on  the  Ayres  Scale  and 
compared  with  Freeman's  average  based  on  a  study  of  handwriting 
in  56  cities.  No  material  difference  appears  between  the  results  in 
Mr.  Harlan's  study  and  the  averages  obtained  by  Freeman,  either  in 
the  quality  or  the  speed  of  writing.  Three  hundred  and  thirty-seven 
pupils  were  tested  in  spelling,  words  being  used  from  the  Ayres  list. 
Results  are  tabulated,  and  Mr.  Harlan  concludes :  "A  comparison  of 
the  above  averages  shows  an  advantage  of  from  seven  to  fourteen 
words  per  one  hundred  in  favor  of  the  city  pupils.  The  country 
averages  are  uniformly  lower  than  the  city  averages.  This  is  no  mere 
statistical  accident.  The  pupils  of  the  rural  schools  do  not  spell  as 
well  on  written  tests  as  do  the  children  of  the  city  schools."  Courtis 
Arithmetic  Tests  Series  B  were  given  to  255  pupils.  The  comparison 
is  with  the  Courtis  Standards.  "In  summarizing,  one  may  say  that  in 
the  fundamental  operations  of  arithmetic  the  pupils  of  the  rural 
schools  rank  approximately  two  grades  below  the  pupils  of  the  city 
schools."  "The  improvement  in  arithmetic  from  grade  to  grade  is 
less  for  country  children  than  for  city  children." 

M.  E.  Haggerty,  in  Studies  in  Arithmetic,  Indiana  University 
Studies,  No.  32  (September,  1916),  reports  results  from  5  counties 
in  Indiana.  Results  are  tabulated,  and  it  is  concluded  that  "These 
data  point  to  the  conclusion  that  the  district  schools  are  more  efficient 
in  procuring  achievement  in  the  function  measured  than  the  graded." 
(p.  68.)  This  is  the  only  study  found  that  reports  an  actual  advan- 
tage in  favor  of  the  rural  school.  Mr.  Paul  Mort  is  directly  responsi- 
ble for  the  data  collected.     It  is  not  definitely  stated  how  the  material 


12  Study  of  Achievement  in  Country  and  Tozvn  Schools 

given  in  this  study  was  gathered,  but  it  is  to  be  inferred  from  the  ex- 
tent of  the  study  that  the  testing  was  done  by  the  teachers. 

In  A  Report  on  the  Use  of  Some  Standard  Tests,  Wisconsin  State 
Department  of  PubHc  Instruction  Studies  in  Educational  Measure- 
ments in  Wisconsin,  Bulletin  No.  1,  W.  W.  Theisen  reports  results 
for  36,564  children  in  Wisconsin,  of  whom  15,825  were  in  rural  schools. 
He  summarizes  on  page  22  as  follows :  "J^^g^^i  ^Y  the  Ayres  stand- 
ards, rural  children  in  Wisconsin  do  not  spell  well.  They  average  not 
less  than  10  points  below  the  standard  in  every  grade.  However, 
when  compared  with  other  classes  of  Wisconsin  schools,  as  will  be 
seen  from  Table  1,  they  are  not  conspicuously  poorer  nor  better  spell- 
ers than  the  pupils  in  the  cities  and  villages." 

The  same  author  in  the  same  report  gives  results  of  penmanship 
scored  according  to  the  Thorndike  Handwriting  Scale  from  141  rural 
schools  in  28  counties.  He  summarizes  (p.  85)  :  "Rural  schools  on  the 
whole  make  the  best  showing  of  Wisconsin  schools  in  writing.  Their 
quality  is  not  inferior  to  that  of  other  classes  of  schools,  and  their 
speed  is  more  nearly  in  accord  with  desirable  standards  in  most  grades." 

The  Sixty-Ninth  Report  of  the  Public  Schools  of  the  State  of  Mis- 
souri (June  30,  1918)  reports  a  series  of  investigations  as  to  rural 
school  conditions  in  that  state.  Courtis  Standard  Reading  Test  No.  2 
was  given  to  6,056  pupils  in  547  schools  in  82  counties.  Among  the 
findings  it  is  stated  (p.  74)  that  "A  second  observation  based  on  the 
table  is  that  in  all  three  phases  of  reading  ability  the  rural  school  chil- 
dren in  these  grades  (2-8)  are  below  the  standard  set  by  Courtis." 

The  Kansas  City  Scale  for  Measuring  Handwriting  was  used  for 
scoring  papers  of  about  8,000  pupils  in  86  counties  in  the  same  state. 
The  results  are  reported  in  detail  by  grades,  and  it  is  concluded  (pp. 
80-81)  that  "The  quality  or  form  of  handwriting  of  the  rural  school 
pupils  is  far  below  the  accepted  standards,  grade  for  grade.  The 
speed  is  above  the  accepted  standards,  except  in  the  seventh  and  eighth 
grades." 

Results  are  also  reported  from  6,445  pupils  in  grades  4  to  8  inclu- 
sive and  from  87  counties  for  the  use  of  Courtis  Standard  Research 
Tests  in  Arithmetic,  Series  B.  (pp.  81-85.)  It  is  concluded  that 
"On  the  whole  the  rural  school  children  in  Missouri  are  not  up  to  the 
ability  of  the  city  pupils  as  shown  by  the  Courtis  general  tabulations. 
This  is  particularly  true  of  the  sixth,  seventh  and  eighth  grades.  In 
the  eighth  grade  it  was  pointed  out  that  the  Missouri  rural  school  pu- 
pils were  below  in  every  particular." 


Previous  Objective  Studies  13 

In  the  same  report  (pp.  85-87)  results  are  given  for  a  spelling  test 
based  on  the  Ayres'  Spelling  Scale  given  to  8,326  pupils  in  611  schools 
in  86  counties.  In  conclusion  it  is  stated  (p.  87)  that  "The  rural 
school  pupils  in  Missouri  are  below  the  standard  attainment  for  the 
city  school  pupils  in  84  of  the  larger  cities  of  the  United  States,  and 
the  writer  of  the  report  of  which  this  section  is  a  summary  says  also 
that  the  rural  school  pupils  are  below  the  attainment  of  the  ten  town 
schools  in  the  state  studied  by  him." 

In  1918,  in  Report  on  Spelling  and  Penmanship  in  Country  Schools, 
Louisiana  State  Department  of  Education,  Bulletin  No.  1,  June, 
1918,  John  M.  Foote  reported  the  results  of  spelling  test  from  the  Ayres 
list  given  to  4,584  pupils  in  rural  schools  in  Louisiana.  He  concludes 
(p.  11)  that :  "While  it  may  be  that  the  superiority  of  the  large  type  of 
school  as  compared  with  the  small  type  is  decisively  reflected  in  the 
instruction  in  some  of  the  subjects  taught,  it  must  be  concluded  that 
in  so  far  as  spelling  ability  in  the  rural  schools  is  concerned  no  such 
decisive  difference  exists.  The  results  show  clearly  that  there  is  a 
difference  in  favor  of  the  large  school,  but  the  assumption  that  the 
classroom  results  are  very  much  better  is  not  warranted." 

The  same  author  in  the  same  bulletin  reports  handwriting  results 
according  to  the  Ayres  Scale  for  4,073  pupils  in  114  rural  schools, 
and  concludes  (p.  24)  that  "It  will  be  seen  by  reference  to  the  table 
and  diagram  that  there  is  comparatively  little  difference  in  both  qual- 
ity and  speed  between  the  five  groups.  It  will  be  noted  that  the  dif- 
ference in  quality  is  less  than  in  speed.  The  situation  is  similar  to  that 
found  in  spelling.  The  evidence  therefore  points  to  the  conclusion 
that  the  pupils  in  the  large  schools  are  sHghtly  superior,  but  that  no 
great  difference  prevails." 

The  same  author,  in  Silent  Reading  in  Rural  and  Village  Schools, 
Louisiana  State  Department  of  Education,  Bulletin  No.  9,  July,  1919, 
reports  results  from  work  with  Monroe's  Standardized  Silent  Reading 
Tests  with  4,315  pupils  in  96  schools  located  in  15  parishes.  He  con- 
cludes (p.  8)  that  "A  comparison  of  the  three  groups  A,  B,  and  C 
reveals  a  distinct  difference  in  favor  of  the  larger  school.  With  the 
exception  of  the  fourth  grade  the  scores  of  group  B  are  better  than 
those  of  group  C.  Group  A  scores  are  higher  in  every  instance  than 
groups  B  and  C.  This  superiority  of  the  large  type  of  school  is  in 
agreement  with  results  reported  for  Santa  Clara  County,  California." 

Still  later,  in  A  Study  of  Arithmetic  in  Rapides  Parish,  Louisiana 
State  Department  of  Education,  Bulletin  No.  11,  September,  1919,  Mr. 


14  Study  of  Achievement  in  Country  and  Town  Schools 

Foote  reports  results  for  the  use  of  the  Courtis  Arithmetic  Test  Series 
B  in  the  schools  of  Rapides  Parish,  Louisiana.  In  this  study  schools 
are  grouped  in  four  classes,  those  in  the  city  of  Alexandria  in  group 
A,  eight  high  schools  in  group  B,  eight  graded  schools  in  group  C,  and 
twenty-eight  one-  and  two-teacher  schools  in  group  D.  Mr.  Foote 
concludes  (p.  12)  that  "Superior  results  are  obtained  in  the  large  type 
of  schools."  (p.  13.)  "Group  A  and  D  vary  in  speed  by  1.0  year 
and  in  accuracy  by  2.0  years.  It  is  therefore  evident  that  the  large 
schools  as  represented  by  groups  A  and  B  obtain  results  that  are  dis- 
tinctly superior  to  those  obtained  by  groups  C  and  D." 

George  A.  Grim,  in  "Spelling  in  Northampton  County,"  University 
of  Pennsylvania  Bulletin,  Vol.  XX,  No.  1,  October,  1919,  Sixth  An- 
nual Schoolmen's  Week  Proceedings,  reports  spelling  results  for  the 
rural  and  urban  sections  of  Northampton  County.  The  results  are 
reported  for  grades  2  to  8  inclusive,  and  in  five  of  the  seven  grades 
reported  the  urban  schools  surpass  the  rural.  The  differences  re- 
ported are  not  great  in  any  case. 

Cyrus  D.  Mead,  in  The  Spelling  Ability  of  the  Plumas  County  Chil- 
dren, California  State  Board  of  Education,  Supplement  of  California 
Blue  Bulletin,  December,  1919,  reports  on  the  spelling  ability  of  the 
pupils  of  Plumas  County,  California,  as  shown  by  a  test  from  the 
Ayres  list.  He  concludes  (p.  5)  that  "The  pupils  of  this  county  are 
.  .  .  just  about  of  the  average  ability  of  city  children  over  the 
country." 

The  above  references  include  all  the  data  easily  available  dealing  in 
an  objective  way  with  the  comparative  results  of  instruction  in  rural 
and  in  urban  schools.  The  difficulty  of  collecting  data  in  rural  schools, 
where  distance  is  great  and  classes  small,  makes  the  time  element  in 
collecting  any  large  number  of  cases  very  great  and  seems  to  have  pre- 
vented the  collection  of  extensive  material.  The  studies  reported  in- 
clude 2  studies  of  composition  work ;  both  of  these  favor  the  urban 
school.  There  are  6  studies  of  handwriting  reported,  and  of  these  3 
favor  the  urban  school,  2  show  negligible  differences,  and  1  favors  the 
rural  school.  Nine  studies  of  arithmetic  are  reported,  and  8  of  these 
favor  the  urban  school,  while  1  favors  the  rural  school.  Four  studies 
of  reading  are  reported,  and  all  of  them  favor  the  urban  school. 
Seven  studies  of  spelling  are  reported,  3  of  which  favor  the  urban 
school  and  4  of  which  find  negligible  differences.  In  all  28  studies  are 
reported,  of  which  20  find  the  results  better  in  urban  schools,  6  find 
negligible  differences,  and  2  find  results  superior  in  the  rural  schools. 


CHAPTER  II 
PURPOSE  AND  SCOPE  OF  THE  PRESENT  STUDY 

The  studies  of  results  of  instruction  in  rural  schools  reported  in 
Chapter  I  are  in  objective  terms,  and  seem  to  indicate  a  situation  that 
is  quite  generally  inferior  to  that  in  cities  and  towns.  All  of  the  com- 
parisons are  made,  however,  upon  a  grade  basis,  which  assumes  that 
the  third  grade,  or  the  eighth  grade,  or  any  other  grade  should  be  the 
same  in  one  system  as  in  another.  That  grades  are  not  in  fact  equal 
is  shown  by  results.  Under  the  present  diversity  of  conditions  it  is 
entirely  possible  that  grades  should  not  be  equal. 

Particularly  is  this  true  in  country  schools  as  contrasted  with  city 
schools.  The  shorter  terms,  poorer  attendance,  and  inherent  difficul- 
ties involved  in  the  small  school  make  it  probable  that  grading  in  these 
schools  should  be  different  from  that  in  city  schools.  For  example, 
in  Madison  County,  Kentucky,  the  school  year  for  the  smaller  schools 
is  only  six  months.  This  means  that  a  boy  or  girl  entering  school  at  the 
age  of  six  and  progressing  normally  would  at  the  age  of  fourteen  com- 
plete the  eighth  grade,  having  attended  school  a  total  of  48  months.  A 
child  entering  one  of  the  larger  schools  of  the  country,  such  as  that  in 
Richmond,  would  have  nine  months'  schooling  each  year,  and  would, 
if  he  progressed  normally,  complete  the  eighth  grade  with  a  total  of  72 
months  in  school;  that  is,  with  24  months'  more  schooling  than  the 
country  child  received. 

Again,  in  some  of  the  states  the  school  system  is  organized  on  the 
basis  of  seven  grades  in  the  elementary  school,  so  that  a  direct  compar- 
ison of  a  fifth  grade  in  a  seven  grade  system  with  a  fifth  grade  in  an 
eight  grade  system  is  impossible. 

Further,  the  use  of  grade  standards  must  assume  that  tests  are  given 
at  the  same  time  in  the  school  year.  This  would  be  necessary  either 
to  compare  the  system  tested  with  another  system  or  with  the  work 
in  the  same  system  in  other  years,  since  the  standard  for  any  grade 
must  be  different  at  the  beginning  and  at  the  close  of  the  school  year. 
It  is  not  always  convenient,  or  even  possible,  to  give  tests  in  any  partic- 
ular part  of  the  school  term.  There  will  be  material  gain  in  the  ease 
of  using  standard  tests  if  it  can  be  made  possible  to  give  them  at  any 
convenient  time  and  to  obtain  results  comparable  with  those  from  other 
places  and  given  at  other  times. 

15 


16  Study  of  Achievement  in  Country  and  Tozvn  Schools 


'• 


Then,  too,  in  any  system  of  schools  some  pupils  are  likely  to  fail  of 
promotion  each  year.  This  causes  retardation,  and  is  much  more  se- 
rious in  some  systems  than  in  others.  Any  consideration  of  the  effi- 
ciency of  a  school  system  must  account  for  this  factor.  Grade  stand- 
ards do  not  do  so. 

It  is  for  such  reasons  as  these  that  the  Nassau  County  Survey,  pub- 
lished as  a  bulletin  of  the  University  of  the  State  of  New  York  (De- 
cember, 1917),  in  reporting  the  measurements  of  the  achievements  of 
pupils,  carefully  refrains  from  making  any  comparison  of  the  urban 
and  rural  schools,  and  makes  the  following  statement  (p.  146)  :  "The 
classification  of  school  districts  by  the  approximate  size  of  the  schools 
has  not  been  continued  in  this  chapter,  because  of  the  possible  injus- 
tice which  might  thereby  be  done  to  the  small  schools,  in  which  the 
exact  classification  of  pupils  into  eight  grades  is  not  always  possible. 
There  might  have  been  possible  a  more  accurate  comparison  of  the 
results  from  large  and  from  small  districts,  if  the  results  had  been 
tabulated  by  age  rather  than  by  school  grade.  A  comparison  of  the 
ability  children  have  in  a  rural  school  by  the  time  they  are  'twelve 
years  old'  with  the  ability  of  children  of  the  same  age  in  a  large  village 
school  might  possibly  be  more  significant  than  a  comparison  of  the 
ability  between  children  of  the  'sixth  grade'  in  the  two  types  of  schools. 
For  several  reasons,  however,  we  have  not  been  able  to  make  such 
comparisons  between  the  achievements  of  pupils  of  the  same  ages  in 
districts  of  various  sizes." 

To  really  measure  school  efficiency  it  is  necessary  to  show  the  prog- 
ress, not  only  of  those  who  are  promoted,  but  of  all  the  children ;  and 
to  do  this  in  terms  of  some  unit  common  to  all  schools,  city  or  country, 
seven  grade  or  eight  grade  system,  and  long  or  short  school  term. 
There  will  be  added  convenience  if  such  a  unit  can  be  so  devised  as 
to  be  usable  at  any  time  during  the  school  year. 

The  chronological  age  of  school  children  is  such  a  unit.  If  the  prog- 
ress made  by  children  can  be  shown,  say  between  the  ages  of  7  and  12, 
a  measure  that  is  definite,  universal,  and  approximately  equal  at  any 
time  during  the  school  year  is  obtained,  provided  only  that  children  of 
both  ages  are  tested  at  the  same  time.  The  question  is  whether  such 
progress  can  be  shown. 

This  study  undertakes : 

First,  to  show  that  the  difference  in  performance  in  school  subjects 
of  children  of  different  ages  can  be  obtained ; 


Purpose  and  Scope  of  Present  Study  17 

Second,  to  show  that  this  difference  is  a  measure  of  school  efficiency 
which  may  be  used  to  measure  schools  or  school  systems ; 

Third,  to  apply  this  measure  to  a  system  of  country  schools ; 

Fourth,  to  compare  the  results  in  this  country  system  of  schools  with 
the  results  in  certain  city  school  systems. 

The  country  school  system  to  which  this  measure  is  applied  is  that 
of  Madison  County,  Kentucky.  This  county  lies  a  little  east  of  the 
central  portion  of  the  state,  and  includes  both  blue-grass  and  mountain 
land.  In  the  1910  census  it  ranks  20th  in  the  land  area  among  the 
counties  of  the  state,  5th  in  the  value  of  all  farm  property,  and  12th 
in  the  value  of  all  farm  crops.  Corn  and  tobacco  are  easily  the  lead- 
ing crops.  The  county  is  one  of  the  wealthier  and  larger  counties  of 
the  state.  There  are  two  normal  schools,  the  Eastern  Kentucky  State 
Normal  at  Richmond  and  a  normal  department  in  connection  with 
Berea  College  at  Berea.  The  number  of  public  white  schools  is  68, 
six  of  which  have  three  or  more  teachers  and  a  term  of  nine  months. 
The  rest  of  the  schools  have  only  one  or  two  teachers  and  a  six-month 
school  year.  A  county  supervisor  of  schools  is  employed  to  assist  the 
county  superintendent.  There  is  no  reason  to  suppose  that  the  schools 
of  this  county  are  particularly  worse  than  those  of  surrounding  counties. 

For  the  purposes  of  this  study  three  tests  were  selected :  Trabue 
Completion-Test  Language  Scale  B,  Courtis  Standard  Research  Tests 
in  Arithmetic  Series  B,  and  Thorndike  Silent  Reading  Scale  Alpha  2. 
These  tests  w'ere  given  in  grades  3  to  8  inclusive  of  all  the  public 
schools  for  white  children  in  the  county  during  November  and  Decem- 
ber, 1919.^  The  results  are  tabulated  separately  for  the  schools  hav- 
ing a  six-month  term  and  for  those  having  a  nine-month  term. 

In  order  that  the  results  in  Madison  County  may  be  compared  with 
results  in  other  places,  data  are  included  as  follows :  From  Louisville, 
Kentucky,  data  for  each  of  the  three  tests  used ;  from  Paterson,  New 
Jersey,  and  St.  Paul,  Minnesota,  data  for  the  Trabue  Language  Scale ; 
from  Louisiana,  Arkansas  City  and  Salina,  Kansas,  and  Hibbing, 
Minnesota,  data  for  the  Courtis  Standard  Research  Tests  in  Arithme- 
tic Series  B ;  from  Hamilton  Township,  New  Jersey,  and  Amsterdam, 
New  York,  data  for  Thorndike  Silent  Reading  Scale  Alpha  2. 

In  order  to  show  clearly  the  method  followed,  the  results  of  the 
Trabue  Completion-Test  Language  Scale  B  are  worked  through  in  de- 
tail in  the  next  chapter. 


^  Five  of  the  one-teacher  schools  were  not  in  session  when  visited,  and  no  re- 
sults from  them  are  given. 


CHAPTER  III 
ACHIEVEMENT  MEASURED  BY  THE  TRABUE  LANGUAGE   SCALE 

Table  I  shows  the  age-grade  distribution  of  scores  made  in  the 
Trabue  Language  Scale  B  by  pupils  in  the  Madison  County  schools 
having  a  term  of  6  months.  The  table  reads  as  follows :  There  are 
8  pupils  7  years  of  age  in  the  third  grade,  1  of  whom  made  a  score  of 
3,  2  a  score  of  4,  2  a  score  of  5,  3  a  score  of  6,  etc.  In  this  table  and 
throughout  the  study  the  age  used  is  that  of  the  last  birthday  at  the 
time  the  test  was  given.  A  child  is  considered  as  10  years  old  who  is 
as  much  as  10  years  old  and  less  than  11  years  old. 

It  is  evident  from  the  total  number  of  cases  occurring  for  the  re- 
spective ages  that  the  distributions  are  incomplete  for  most  ages ;  prob- 
ably for  all.  There  should  be  at  least  as  many  8-year-old  children,  for 
example,  as  there  are  9-year-olds.  This  incompleteness  for  the  younger 
ages  represents  children  in  the  first  and  second  grades,  which  were  not 
tested,  or  children  who  have  not  yet  entered  school.  Since  these  chil- 
dren have  not  yet  been  promoted  to  the  third  or  higher  grades,  it  is 
evidently  the  opinion  of  the  teachers  that  they  could  not  do  so  well  as 
the  children  who  are  in  the  third  or  higher  grades.  It  follows  that  the 
distributions  for  children  of  the  younger  ages  are  lacking  in  the  num- 
ber of  cases  for  the  lower  scores.  The  distributions  for  the  older 
children,  on  the  other  hand,  may  be  considered  as  lacking  in  the  num- 
ber of  cases  for  the  higher  scores,  since  the  older  children  not  appear- 
ing in  the  table  are  those  who  have  either  completed  the  eighth  grade 
before  reaching  the  age  indicated,  or  who  have  for  some  reason  stopped 
attending  school. 

If  the  difference  in  performance  in  school  subjects  of  groups  of 
children  of  different  ages  is  to  be  a  valid  measure  of  the  efficiency  of 
a  school  system,  it  is  evident  that  the  age-groups  in  the  respective  sys- 
tems must  be  comparable.  That  is  to  say,  either  these  groups  must 
include  all  children  of  the  age  indicated,  or  the  selection  must  be  shown 
to  be  by  random  sampling  only,  or  the  selection  must  be  shown  to  be 
influenced  only  by  known  causes  acting  equally  and  in  the  same  direc- 
tion, or  it  must  be  possible  to  so  correct  the  age-groups  given  as  to 
meet  substantially  the  above  conditions. 

The  age-groups  presented  in  Table  I  do  not  meet  the  first  of  these 

18 


TABLE  I :  Age-Grade  Distribution  of  Trabue  Language  Scale  B  Scores  in 
THE  6-MoNTH  White  Schools  of  Madison  County,  Ky.  (November  and 
December,  1919) 


Age 

Grade 

SCOEES 

Total 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

7 

3 

4 
5 

1 

2 
2 
1 

2 

1 

3 

1 
1 

8 

1 

1 

6 

2 

Total 

1 

1 

5 

3 

5 

1 

16 

8 

3 
4 
5 

6 

1 

2 
1 

1 
1 

3 
3 

2 

1 

10 

7 

1 

'""4 

2 

1 

4 

1 

27 

1 

1 

.... 

.... 

1 

22 

5 

7 

Total 

3 

2 

6 

3 

18 

4 

7 

1 

1 

1 



1 

54 

9 

3 
4 
5 

6 
6 

6 
2 
1 

... 
"1 

12 

1 

2 
3 

9 
7 
4 

3 

2 

2 
3 

7 

40 

3 
4 

2 
1 

3 

.... 

1 
1 

33 

20 

Total 

12 

9 

1 

13 

5 

20 

5 

12 

7 

3 

3 

1 

2 

93 

10 

3 
4 
5 
6 

7 
8 

3 

1 

1 

1 
"2 

1 

5 
3 
2 

1 
2 
3 

9 
6 
4 
1 
1 
1 

1 
2 
4 
2 

4 
8 
3 
2 

'"'3 
5 

1 

1 

2 
3 

1 

2 
3 
4 
2 

1 
.... 

30 

1 
2 

31 

32 

1 

11 

1 

1 

2 



Total 

4 

1 

3 

1 

10 

6 

22 

9 

17 

9 

7 

11 

2 

4 

1 

107 

11 

3 

4 
5 
6 
7 
8 

3 

1 

3 
1 
1 

.;; 

3 
3 

2 

"i 

3 

2 

5 
10 
3 

1 

2 
1 
3 

1 
2 
4 

1 
2 

1 
4 
3 

1 

1 
4 
1 

1 

19 

3 
4 
5 
1 

1 
5 
2 

28 

2 

34 

.... 

i 

2 

.... 

.... 

16 

5 

1 

_.-. 

1 

.... 

2 

4 

Total 

5 

8 

6 

19 

6 

10 

8 

13 

8 

8 

2 

1 

3 

2 

1 

104 

12 

3 
4 
5 
6 

7 
8 

1 
1 

1 

1 

1 
1 
2 

1 

"2 

1 

3 
9 

8 

1 

2 

4 

3 

.... 

10 

3 
5 
3 

6 

2 

6 
2 
1 

1 
4 
4 
7 
2 

25 

1 

5 

1 

2 
4 

2 

2 
1 

2 

31 

-- 

1 

1 

1 
1 

27 

16 

3 

7 

1 

Total 

0 

■> 

4 

4 

21 

10 

11 

17 

7 

8 

18 

6 

3 

.... 

3 

116 

13 

3 
4 
5 
6 

7 
8 

1 

.-. 

3 

1 

1 
1 

'  "i 
1 
1 

1 

2 
7 
3 

1 

2 
4 
5 

6 

9 
.... 

1 
4 
2 
2 
1 

2 
2 
6 

2 

1 

2 
2 
1 

""'2 

1 

— - 

.... 

.... 

16 

27 

2 
3 
1 

2 
""4 

1 

2 
5 

23 

2 

12 

1 

16 

Total 

2 

4 

2 

3 

14 

9 

10 

12 

13 

7 

6 

7 

8 

2 

1 

.... 

100 

14 

3 
4 
5 
6 
7 
8 

1 

1 

1 

2 
3 
2 
2 

3 

2 

"i 

1 
2 
2 

5 
2 
1 
2 
2 

1 

2 

1 

.... 

11 

3 
3 
2 
2 

1 
.... 

1 

2 
3 
2 
6 

1 
1 
2 
5 

18 

15 

1 

1 
2 

13 

1 

--. 

... 

.... 

22 

Total 

3 

1 

1 

2 

5 

5 

12 

10 

5 

10 

3 

13 

9 

3 

82 

15 

3 

4 
5 
6 
7 

8 

1 

---- 

I 

2 

1 
1 

1 

1 

3 

1 

.... 

— - 

2 

1 
1 
4 

1 
1 
1 

1 
1 
2 

3 

3 

2 

'""3 

6 

1 

3 

1 

17 

Total 

2 

1 

2 

2 

7 

3 

5 

3 

4 

3 

1 

33 

16 

4 
5 
6 
7 
8 

1 

1 

2 

2 

2 
1 

3 
1 

3 
4 

1 

9 

1 

1 

4 

4 

16 

Total 

_. 



1 

1 

2 

1 

4 

3 

4 

7 

1 

4 





28 

19 


20  Study  of  Achievement  in  Country  and  Town  Schools 

conditions,  in  that  they  do  not  include  all  the  children  of  the  ages 
indicated.  Take,  for  example,  the  group  of  12-year-old  children,  the 
largest  group  presented.  This  shows  10  children  in  the  third  grade, 
25  in  the  fourth,  31  in  the  fifth,  27  in  the  sixth,  16  in  the  seventh,  and 
7  in  the  eighth.  Since  the  distribution  of  12-year-old  children  through- 
out the  grades  is  not  rectilinear,  as  is  shown  by  the  part  of  the  distri- 
bution given,  it  seems  unlikely  that  if  a  full  distribution  were  available 
it  would  stop  at  the  lower  end  with  10  children  in  the  third  grade  or 
at  the  upper  end  with  7  children  in  the  eighth  grade.  It  seems  likely 
that  there  would  be  some  12-year-old  children  in  grades  below  the 
third  and  in  grades  above  the  eighth.  This  opinion  in  the  latter  in- 
stance is  substantiated  by  the  fact  that  some  10-  and  11-year-old  chil- 
dren are  in  the  eighth  grade  this  year.  If  they  progress  normally, 
they  will  complete  the  work  of  the  elementary  school  this  year,  and 
will  not  be  enrolled  in  the  school  next  year.  The  same  thing  is  likely 
to  have  happened  last  year,  so  that  there  are  now  some  children  who 
are  12  years  old  and  have  completed  the  work  that  the  school  offered 
and  are  therefore  not  in  school.  Also,  there  are  13-,  14-,  and  even  15- 
year-old  children  in  the  third  grade.  There  is  every  reason  to  sup- 
pose that  there  are  12-year-old  children  in  grades  lower  than  the  third. 
In  addition  to  the  above  considerations,  it  is  known  that  there  were 
some  children  absent  from  school  on  the  day  the  tests  were  given. 

As  regards  the  second  possibility  mentioned  for  comparable  groups : 
Is  the  selection  by  random  sampling  only?  In  so  far  as  the  selection 
is  due  to  absence  from  school  on  the  day  the  test  was  given,  the  se- 
lection may  be  considered  random  as  to  ability  in  the  test  concerned. 
The  chief  causes  of  absence  mentioned  by  the  teachers  were  work,  bad 
weather,  illness,  and  indifference  on  the  part  of  the  parents.  The 
work  for  which  the  children  were  kept  at  home  during  the  time  these 
tests  were  being  given  (November  and  December)  was  usually  work- 
ing tobacco  or  killing  hogs.  While  it  is  likely  that  more  of  the  older 
children  than  of  the  younger  ones  were  kept  at  home  for  work,  still 
some  of  the  younger  ones  were  kept  at  home  for  this  purpose.  The 
discrepancy  in  absences  between  the  older  and  younger  children  in  re- 
gard to  absence  for  work  is  reversed  and  probably  neutralized  by  the 
discrepancy  in  absences  due  to  bad  weather  and  roads.  The  absences 
due  to  illness  of  the  children  and  to  indifference  on  the  part  of  the 
parents  may  be  assumed  to  be  about  the  same  for  children  of  all  ages. 

On  the  other  hand,  the  selection  due  to  the  inclusion  of  only  those 
children  in  grade  3  to  8  inclusive  is  not  random.     The  older  children 


Achievement  Measured  by  Trabue  Language  Scale  21 

in  grades  1  and  2,  that  is,  those  who  are  not  included  in  the  distribu- 
tion given,  are  in  those  grades  because,  in  the  opinions  of  the  teachers, 
they  are  not  so  able  as  the  children  of  the  higher  grades,  or  because 
they  have  for  some  reason  become  so  retarded  in  their  school  work  as 
to  make  them  distinct  from  other  children.  In  other  words,  these 
children  are,  in  the  opinions  of  the  teachers,  of  less  ability  in  school 
work  than  those  of  corresponding  age  who  have  been  promoted  to  the 
higher  grades.  This  means  that  the  distributions  given  in  Table  I 
do  not  include  the  children  who  have  the  lower  degrees  of  ability  in 
school  work.  In  the  same  way  the  younger  children  who  have  com- 
pleted the  eighth  grade  and  are  therefore  not  included  in  the  table  are, 
in  the  opinions  of  the  teachers,  the  children  having  the  higher  degrees 
of  ability  in  school  work.  All  of  which  goes  to  show  that  the  selec- 
tion of  cases  for  the  age-groups  as  they  are  presented  is  not  random. 

The  next  consideration  is  whether  the  selection  of  age-groups,  in 
such  respects  as  it  is  not  random,  is  due  to  the  same  causes  acting 
equally  and  in  the  same  direction,  for  all  the  schools  to  be  measured, 
and  in  each  of  the  age-groups.  As  is  shown  above,  there  is  decided 
selection  due  to  the  failure  to  include  children  in  grades  1  and  2,  and 
those  who  have  completed  the  eighth  grade.  This  number  of  children 
is  determined  by  the  rate  of  progress  of  children  through  the  grades. 
This  rate  of  progress  is  unequal  even  for  different  schools  within  the 
same  system,  as  has  been  shown  repeatedly  by  studies  widely  sepa- 
rated both  in  time  and  locality.  A  good  and  recent  example  is  fur- 
nished by  the  age-grade  tables  on  page  90  of  An  Educational  Study  of 
Alabama,  United  States  Bureau  of  Education  Bulletin,  1919,  No.  41. 

The  possibility  still  remains  of  correcting  the  tables  presented.  In 
order  to  correct  an  incomplete  distribution  such  as  that  presented  it 
is  necessary  to  have  a  reasonably  large  part  of  the  complete  distribu- 
tion. In  the  data  presented  the  most  nearly  complete  distributions  are 
those  for  the  ages  10,  11,  12  and  13.  The  distribution  of  12-year- 
olds  is  the  largest  given,  which  indicates  that  it  is  most  nearly  complete. 
Taking  this  distribution  as  a  sample,  how  may  it  be  corrected  ? 

Unfortunately  the  form  of  this  distribution  is  not  exactly  that  of 
the  normal  frequency  curve.  This  is  shown  by  that  portion  of  the 
distribution  which  is  given.  It  might  also  be  inferred  from  the  fact 
that  in  most  school  systems  it  is  easier  for  a  child  to  become  retarded 
than  it  is  for  a  child  to  make  two  grades  in  one  year.^     This  natu- 


^  Strayer  and  Thorndike,  Educational  Administration,  p.  38. 


22  Study  of  Achievement  in  Country  and  Town  Schools 

rally  causes  a  skewed  distribution.  To  correct  a  skewed  distribution  for 
truncation  by  the  development  of  mathematical  formulae  is  a  lengthy 
and  complicated  process,  and  one  that  is  liable  to  serious  error.  Fur- 
ther, since  the  degree  of  skewedness  and  of  truncation  may  both  vary 
for  every  distribution  to  be  studied,  such  correction  is  obviously  too 
tedious  and  cumbersome  a  method  to  be  used  in  a  measure  of  school 
efficiency  that  is  to  be  easily  available  for  busy  school  men. 

If  an  age-grade  table  of  all  the  children  in  all  the  grades  were  avail- 
able, it  might  serve  as  a  basis  for  calculating  the  number  of  children  in 
grades  1  and  2.  It  does  not  furnish  a  ready  basis  for  finding  the  num- 
ber who  have  completed  the  eighth  grade.  Also,  for  Madison  County 
schools  no  such  table  is  available.^ 

The  problem  resolves  itself  into  an  attempt  to  find  the  number  of  12- 
year-old  children  who  are  in  either  the  first  or  second  grade,  or  who 
have  completed  the  eighth  grade.  The  13-year-old  children  in  the 
third  grade  this  year  probably  were  in  the  second  grade  last  year  when 
they  were  12  years  old.  The  probability  is  that  last  year  the  number 
of  12-year-old  children  in  the  second  grade  who  were  not  promoted 
to  the  third  grade  was  about  equal  to  the  number  of  13-year-old  chil- 
dren in  the  third  grade  who  were  not  promoted  to  the  fourth  grade. 
Inasmuch  as  there  has  been  no  particular  change  in  the  school  popu- 
lation of  Madison  County  during  the  last  few  years,  and  in  view  of 
the  above  probabilities,  the  number  of  13-year-old  children  in  the 
third  grade  may  be  considered  a  fairly  reliable  indication  of  the  num- 
ber of  12-year-old  children  in  the  second  grade. ^  Reference  to  Table 
I  shows  this  number  to  be  6.  Similarly,  the  14-year-old  children  in 
the  third  grade  may  be  considered  a  measure  of  the  12-year-olds  in 
the  first  grade.     This  number  is  3. 

In  much  the  same  way  it  may  be  supposed  that  the  number  of  11- 


^To  get  a  census  showing  the  ages  of  children  in  the  first  and  second  grades 
of  the  Madison  County  public  schools  it  would  be  necessary  to  visit  each  school, 
and  in  the  case  of  children  who  do  not  know  their  age,  to  visit  the  home. 

'  In  order  to  test  the  validity  of  this  assumption  a  study  was  made  of  the 
age-grade  tables  for  rural  children  and  for  children  in  places  having  a  popula- 
tion of  less  than  2,000  given  on  page  90  of  An  Educational  Study  of  Alabama, 
United  States  Bureau  of  Education  Bulletin,  1919,  No.  41,  and  the  age-grade 
table  for  pupils  in  non-city  schools  given  on  page  309  of  the  Survey  and  Report 
of  the  Virginia  Public  Schools  Education  Commission.  The  actual  number  of 
10-,  11-,  12-  and  13-year-old  children  in  grades  1  and  2  was  compared  with  the 
number  of  such  children  estimated  to  be  in  these  grades  on  the  basis  of  the 
above  assumption.  The  difference  between  the  actual  number  of  such  children 
and  the  estimated  number  was  reduced  to  a  percentage  basis  showing  the  per 
cent  of  error  in  each  estimate.  Twenty-four  estimates  were  made,  and  the 
median  per  cent  of  error,  direction  of  error  being  taken  into  account,  was  — 4j^. 


Achievement  Measured  by  Trabue  Language  Scale  23 

year-old  children  in  the  eighth  grade  this  year  is  the  same  as  the  num- 
ber of  11 -year-old  children  in  the  eighth  grade  last  year.  These  should 
be  added  to  the  12-year-old  distribution  this  year.  Reference  to  Table 
I  shows  this  number  to  be  2.  In  the  same  way  the  number  of  children 
who  are  12  years  old  this  year  and  who  completed  the  eighth  grade 
two  years  ago  is  estimated  as  2. 

Using  these  estimates,  the  following  distribution  of  12-year-old  chil- 
dren is  obtained:  3  in  grade  1,  Language  Scale  scores  unknown;  116 
in  grades  3  to  8  inclusive,  distributed  according  to  Language  Scale 
scores ;  2  who  completed  grade  8  last  year,  Language  Scale  scores  un- 
known ;  and  2  who  completed  grade  8  two  years  ago,  Language  Scale 
scores  unknown. 

Estimating  corrections  for  the  10-,  11-  and  13-year-old  distributions 
on  the  same  basis  as  for  the  12-year-olds,  gives  Table  IL  In  this 
table  the  figures  in  the  columns  under  the  captions  XI,  X2,  X9,  XIO, 
and  XI 1  are  the  estimated  number  of  children  of  the  respective  ages 
in  grades  1,  2,  9,  10  and  11  respectively.^ 

These  corrections  make  the  distributions  for  the  ages  10,  11,  12  and 
13  reasonably  complete.  There  is  still  some  elimination  of  children  in 
the  grades  to  be  accounted  for,  and  there  is  the  possibility  that  some 
of  the  children  of  these  ages  may  not  have  entered  school.  These 
considerations  are  probably  not  so  serious,  however,  as  the  fact  that 
the  scores  of  the  children  represented  by  estimated  additions  to  the 
distributions  are  unknown.  It  is  known,  however,  that  the  children 
in  the  lower  grades  are  likely  to  have  made  very  low  scores,  while, 
on  the  contrary,  the  children  who  have  completed  the  eighth  grade 
would  probably  have  made  relatively  high  scores.  Allowing  these 
cases  to  remain  undistributed  at  the  respective  ends  of  the  distribution, 
the  medians,  Q's  and  P.E.'s  of  Table  II  are  obtained. 

The  distributions  of  scores  in  this  table  show  a  great  amount  of 
overlapping  for  the  different  ages.  Twenty  per  cent  of  the  children 
in  the  10-year-old  group  have  scores  superior  to  those  of  50  per  cent 
of  the  13-year-old  children.  This  overlapping  is  in  accord  with  the 
results  obtained  with  grade  distributions. 


^An  attempt  was  made  to  estimate  the  necessary  additions  for  these  distribu- 
tions on  the  basis  of  an  age-grade  table  showing  a  form  of  distribution  similar 
to  that  in  Madison  County.  The  age-grade  table  for  the  Alabama  schools  in 
places  of  less  than  2,000  population  was  used.  No  estimate  of  children  who 
had  completed  the  eighth  grade  seemed  feasible  on  this  basis,  and  the  medians 
calculated  on  the  basis  of  the  distributions  corrected  in  this  way  showed  co- 
efficients of  unreliability  greater  in  every  instance  than  those  of  the  medians  cal- 
culated on  the  basis  of  the  above  corrections. 


24  Study  of  Achievement  in  Country  and  Town  Schools 


As  in  the  overlapping  of  grade  distributions,  so  in  this  overlap- 
ping with  age  distributions,  the  unreliability  of  the  individual  measures 
gives  an  indication  of  greater  overlapping  than  really  exists.^  In  this 
case  there  is  an  added  element  tending  to  exaggerate  the  amount  of 
overlapping  in  the  undistributed  scores  at  both  ends  of  the  age  distri- 
butions. These  scores  tend  to  increase  the  inter-quartile  range,  and 
consequently  the  Q. 

TABLE  II 

Age  Distribution,  10  to  13  Inclusive,  of  Trabue  Language  Scale  B  Scores 
IN  the  6-Month  White  Schools  of  Madison  County,  Ky. 


Scores 

Age 

Total 

XI 

10 
6 
3 

X2 

19 
10 
6 

0 

4 
4 
2 

1 
1 

"i 

2 

3 
5 

9 

3 
1 

4 

10 

8 
4 

5 

6 
6 
4 

6 

22 
19 
21 

7 

9 
6 
10 

8 

17 
10 
11 

9 

9 

8 
17 

10 

7 
13 

7 

11 

11 

8 
8 

12 

2 
8 
18 

13 

4 

2 
6 

14 

1 
1 

2 

15 

16 

17 

18 

X9 

XIO 

Xll 

in 

136 

11 

3 

2 
3 

1 

2 
2 

122 

12 

2 

129 

13 

2 

3 

2 

4 

2 

3 

14 

9 

10 

12 

13 

7 

6 

7 

8 

2 

- 

1 

7 

2 

2 

116 

P.  E.  true 

Median 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.  E. 

in 

6.63 

.37 

9.00 

2.00 

3.50 

M11-M10=  .87 

.311 

11 

7.50 

.34 

10.73 

4.68 

3.02 

M12-M11  =  1.52 

.283 

12 

9.02 

.30 

12.04 

6.48 

2.78 

M13— M12=  .73 

.305 

13 

9.75 

.35 

13.00 

6.92 

3.03 

M13— M10=3.12 

.316 

Another  notable  feature  of  this  table  is  the  great  discrepancy  be- 
tween progress  at  different  ages.  The  improvement  the  11 -year-old 
children  show  over  the  10-year-olds  is  .87  of  a  step ;  that  of  the  12- 
year-olds  over  the  11-year-olds  is  1.52;  and  that  of  the  13-year-olds 
over  the  12-year-olds  is  .73  of  a  step.  The  progress  in  language  ability 
as  measured  by  this  test  is  almost  as  great  from  ages  11  to  12  as  the 
combined  progress  from  ages  10  to  11  and  from  ages  12  to  13. 

The  total  progress  for  the  three-year  period  from  10  to  13  inclusive 
is  3.12  with  a  P.E.  of  .316.-  Since  these  schools  were  in  session  for 
6  months  each  year,  the  total  school  time  for  the  three  years  is  18 
months.  This  makes  the  average  progress  per  month  for  the  period 
.173  of  a  step. 

The  results  of  the  Trabue  Language  Scale  B  test  in  the  white  schools 
of  Madison  County  having  a  9-month  school  term  are  handled  in  the 


^  Thorndike,  E.  L. :  Mental  and  Social  Measurements,  p.  93.  Kelley,  T.  L. : 
"The  Measurement  of  Overlapping,"  Journal  of  Educational  Psychology,  X : 
458#.  (December,  1919). 

^  Thorndike :  Mental  and  Social  Measurements,  p.  194. 


Achievement  Measured  by  Trabue  Language  Scale 


25 


same  way  as  are  those  from  the  schools  having  a  6-month  school  term. 
Table  III  gives  the  facts  for  these  schools. 

From  this  table  it  seems  that  the  overlapping  of  language  perform- 
ance of  children  of  different  ages  is  about  as  great  in  the  9-month 
schools  as  in  the  6-month  schools.  Some  of  the  10-year-old  children 
have  scores  above  the  median  score  of  the  13-year-olds.  The  same 
causes  are  operating  to  make  this  overlapping  appear  greater  than  it 
really  is. 

TABLE  III 

Age  Distribution,  10  to  13  Inclusive,  of  Trabue  Language  Scale  B  Scores 
IN  THE  9-Month  White  Schools  of  Madison  County,  Ky. 


Scores 

Age 

Total 

XI 

X2 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

X9 

XIO 

XI 1 

10 

9 
2 
3 

17 
9 
2 

2 
7 
5 

— 

2 
2 
2 

"i 

1 

8 
3 
6 

7 
4 
3 

18 
14 

8 

7 
6 
4 

17 
16 

8 

8 
5 
14 

12 
8 
12 

8 
5 
12 

8 

7 

12 

3 
4 
15 

1 
3 
10 

2 
2 
11 

1 

1 
7 

1 
1 
1 

132 

11 

"\ 

1 

1 

101 

12 

1 

139 

13 

4 

3 

7 

1 

2 

4 

4 

10 

9 

5 

7 

9 

11 

11 

2 

-- 

10 

1 

1 

101 

P.  E. tru 

e 

Median 

— obtaine 
median 

d 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

7.42 

.32 

10.33 

4.37 

2.98 

Mil— M10=  .73 

.290 

U 

8.15 

.31 

10.84 

5.31 

2.76 

M12— Mll=2.97 

.284 

12 

11.12 

.30 

13.81 

8.09 

2.86 

M13— M12  =  1.09 

.295 

13 

12.21 

.36 

14.97 

9.02 

2.97 

M13— M10  =  4.79 

.304 

Note. — In  these  and  succeeding  tables  XI  is  the  estimated  number  in  grade  1, 
scores  unknown.  X2,  X9,  XIO  and  XI 1  represent  the  corresponding  facts  for 
grades  2,  9,  10  and  11  respectively.  MIO  is  the  median  for  10-year-old  children, 
age  last  birthday  at  the  time  the  test  was  given.  Mil,  M12  and  M13  are  the 
medians  for  the  ages  11,  12  and  13  respectively. 

Also,  the  progress  between  the  different  ages  is  unequal,  as  in  the 
case  of  the  children  in  the  6-month  schools.  The  improvement  between 
ages  10  and  11  is  .73  of  a  step;  between  ages  11  and  12  it  is  2.97  steps; 
and  between  ages  12  and  13  it  is  1.09  steps.  The  total  improvement  for 
the  three-year  period  from  ages  10  to  13  inclusive  is  4.79  steps,  with  a 
P.E.  of  .304.  Since  there  are  9  months  of  school  each  year,  the  total 
school  time  represented  is  27  months.  The  average  monthly  improve- 
ment, therefore,  is  .177  of  a  step.  The  corresponding  improvement 
for  the  6-month  schools  is  .173  of  a  step. 

This  comparison  would  be  valid  and  significant  if  it  could  be  as- 
sumed that  the  quality  measured,  ability  to  complete  correctly  sen- 
tences in  which  certain  words  are  missing,  was  improved  only  by  school 


26         Study  of  Achievement  in  Country  and  Totvn  Schools 

work.  Such,  however,  is  not  known  to  be  the  case.  It  is  entirely 
possible  that  this  quality  improves  by  a  natural  development  as  the  age 
and  experience  of  the  subject  increases.  It  is  possible,  and  even  prob- 
able, that  this  ability  to  complete  sentences  is  improved  both  by  natural 
development  and  by  school  work.  The  conclusion  from  the  above 
comparison,  therefore,  is  that  schooling  and  natural  development  ac- 
complish an  improvement  of  this  ability  of  4.79  steps  between  the 
ages  of  10  and  13  inclusive  for  the  children  in  places  in  Madison 
County  having  a  9-month  school  term,  and  of  3.12  steps  in  places  in 
the  same  county  having  a  6-month  school  term. 


TABLE  IV 

Age  Distribution,  10  to  13  Inclusive,  of  Trabue  Language  Scale  B  Scores 
IN  Certain  White  Schools  of  Louisville,  Ky. 


Scores 

Total 

XI 

4 

1 

X2 

12 
4 
1 

X3 

36  - 
12 

4  . 

1  - 

0    1 

2 

3 

4 

1 
4 
2 
2 

5 

"i 

1 

6 

8 
5 
2 
3 

7 

2 
1 
3 

1 

8 

18 
13 
21 
10 

9 

4 
6 
3 
5 

10 

32 
39 
19 

22 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

X9 

10 
11 

17 
9 
12 

8 

43 
55 
43 
53 

17 
11 
19 
13 

29 
67 

77 
65 

6 
13 
16 

27 

14 

26 
70 
46 

1 
1 
4 
6 

3 
17 
27 
20 

247 

? 

1 

6 
4 

7 

"26 

292 

19 

332 

n 

316 

P.  E. true 

Median 

—obtained 

75  per 

25  per- 

Q 

P.E. 

— 

mediad 

centile 

centile 

10 

11.32 

.24 

13.48 

7.37 

3.11 

Mil— M10=1.58 

.174 

11 

12.90 

.14 

14.37 

10.36 

2.00 

M12— Mll  =  1.56 

.120 

1' 

14.46 

.13 

16.37 

12.34 

2.01 

M13— M12=  .15 

.120 

13 

14.61 

.14 

16.58 

12.50 

2.04 

M13— M10=3.29 

.174 

Table  IV  gives  the  facts  in  regard  to  the  Trabue  Language  Scale  B 
test  for  certain  of  the  white  schools  of  Louisville.  The  papers  on 
which  this  table  is  based  were  given,  collected  and  scored  by  the 
Psychological  Laboratory  of  the  Louisville  Board  of  Education. 

The  total  improvement  in  ability  to  complete  sentences  in  these 
schools  for  the  three-year  period  from  ages  10  to  13  inclusive  is  3.29. 
The  P.E.  of  this  gain  is  .174,  a  little  over  5  per  cent  of  the  gain.  The 
probable  deviation  of  the  true  measure  of  this  gain  from  the  measure 
obtained  is  only  about  half  as  great  as  in  the  Madison  County  schools, 
either  those  having  a  9-month  school  term  or  those  having  a  6-month 
term.  The  total  gain  made  is  a  little  greater  than  in  the  case  of  the 
Madison  County  6-month  schools  and  is  not  quite  so  great  as  in  the 
case  of  the  Madison  County  9-month  schools.  The  median  ability  of 
the  respective  age-groups,  on  the  other  hand,  is  materially  higher  than 


Achievement  Measured  by  Trabue  Language  Scale 


27 


is  the  case  in  any  of  the  Madison  County  schools.  The  median  for  the 
Louisville  10-year-old  children  is  higher  than  for  any  of  the  age-groups 
of  the  6-month  schools,  and  is  higher  than  all  except  the  13-year-old 
group  for  the  9-month  schools.  The  median  ability  of  the  Louisville 
13-year-old  group  is  14.61 ;  that  for  the  Madison  County  9-month 
schools  of  corresponding  age  is  12.21,  and  for  the  6-month  schools  is 
9.75.  The  13-year-old  children  in  Louisville  have  an  ability  to  com- 
plete sentences  that  is  50  per  cent  greater  than  the  like  ability  of  chil- 
dren of  the  same  age  in  the  6-month  schools  of  Madison  County. 

The  progress  made  each  year  in  the  Louisville  schools  is  unequal, 
as  is  the  case  in  the  Madison  County  schools.  In  Louisville  the  prog- 
ress from  10  to  11  is  1.58;  from  11  to  12  it  is  1.56;  and  from  12  to  13 
it  is  .15. 

TABLE  V 

Age  Distribution,  10  to  13  Inclusive,  of  Trabue  Language  Scale  B   Scores 

IN  Paterson,  N.  J. 


Scores 

Arp, 

Total 

XI 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

,8 

19 

X9 

XIO 

in 

---- 

5 

2 

7 

1 

2 
"3 

5 
6 

4 
4 
2 

23 
11 

8 

18 
10 

8 

31 
17 
15 

20 
16 
Ifi 

34 
34 
39 

23 
27 
19 

15 
29 
32 

13 

18 
25 

4 
11 

18 

2 
4 
9 

1 

7 
9 

209 

11 

2 
3 

2 
3 

1 
1 

200 

12 

1 

8 

224 

in 

2 

1 

1 

2 

6 

2 

14 

13 

25 

20 

29 

26 

17 

16 

12 

9 

1 

42 

8 

246 

P.  E. true 

Median 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

9.03 

.12 

10.01 

7.02 

1.49 

Mil— M10  =  2.27 

.128 

11 

11.30 

.16 

12.82 

9.06 

1.88 

M12— Mll=  .48 

.141 

n 

11.78 

.16 

13.80 

9.87 

1.% 

M13— M12=1.52 

.180 

13 

13.30 

.24 

16.87 

10.82 

3.02 

M13-M10=4.27 

.170 

Table  V  gives  the  facts  in  regard  to  the  Trabue  Language  Scale  B 
for  schools  in  Paterson,  New  Jersey.  The  data  from  which  this  table 
is  compiled  were  collected  by  the  department  of  school  administration 
of  Teachers  College,  Columbia  University. 

The  total  gain  in  ability  to  complete  sentences  in  the  Paterson  schools 
is  4.27.  This  gain  is  greater  than  in  the  case  of  any  other  schools  pre- 
sented in  this  study.  The  P.E.  of  this  gain  is  .170,  which  is  about  the 
same  as  that  for  the  like  measure  in  Louisville.  Since  the  gain  in  this 
case  is  greater,  the  proportion  of  the  probable  error  to  the  gain  is  a 
little  less ;  in  Paterson  4  per  cent  as  against  a  little  more  than  5  per 
cent  in  Louisville.  The  median  ability  of  the  13-year-old  children  in 
the  Paterson  schools  is  13.30  as  against  14.61  in  the  Louisville  schools. 


28         Study  of  Achievement  in  Country  and  Town  Schools 


CHART  I 
Progress  in  Trabue  Language  Completion  Test  Scores  Between  Age 
Groups  in  the  Public  Schools  of  Madison  County,  Ky.  ;  Louis- 
ville, Ky. ;  Paterson,  N.  J.;  and  St.  Paul,  Minn. 


SCORES 
161 


A6ES  lO 


12 


Achievement  Measured  by  Trahue  Language  Scale 


29 


This  median  ability  of  the  13-year-old  children  in  Paterson,  however, 
is  greater  than  is  the  like  measure  for  the  6-month  or  the  9-month 
schools  of  Madison  County. 

The  yearly  gains  are  again  unequal.  From  10  to  11  the  gain  is 
2.27;  from  11  to  12  it  is  .48;  and  from  12  to  13  it  is  1.52. 

Table  VI  gives  the  facts  in  regard  to  the  Trabue  Language  Scale  B 
in  St.  Paul,  Minnesota.  This  table  is  based  upon  data  printed  in  the 
St.  Paul  Survey. 

TABLE  VI 

Age  Distribution,  10  to  13  Inclusive,  of  Trabue  Language  Scale  B  Scores  in 
St.  Paul,  Minn.    Based  on  Tables  Published  in  the  St.  Paul  Survey 


Scores 

Total 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

X9 

10 

4 

1 

-- 

15 
2 

1 
2 

4 
1 

1 
1 

19 
8 
3 
5 

9 
6 
4 
1 

30 
24 
13 
10 

24 
8 

13 
11 

56 
39 
42 
21 

33 
25 
21 
16 

63 
53 
55 
41 

41 
30 
39 
39 

52 
53 
77 
61 

26 
35 
45 
54 

24 
50 
50 
66 

12 
8 

30 
40 

4 
11 

20 
29 

1 
3 
4 
14 

417 

11 

12 
13 

"4 

7 

2 

-— 

359 
422 

1 

38 

453 

Median 

P.  E.  true 

—obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

10.32 
11.41 
12.24 
13.34 

.13 
.14 
.11 
.12 

12.28 
13.55 
14.05 
15.29 

7.96 
9.03 
10.13 
11.13 

2.25 
2.26 
1.96 
2.08 

M11-M10=1.18 
M12— Mll=  .83 
M13— M12=1.10 
M13— M10=3.11 

.120 
.106 
.098 
.106 

The  total  gain  in  ability  to  complete  sentences  in  this  case  is  3.11. 
This  gain  is  less  than  in  any  of  the  other  systems  studied.  The  median 
ability  of  the  13-year-old  children,  on  the  other  hand,  is  13.34,  which 
is  higher  than  the  like  ability  of  the  same  age-group  in  any  of  the  other 
systems  studied  except  Louisville.  The  P.E.  of  the  gain  in  these 
schools  is  .106,  which  is  less  than  4  per  cent  of  the  gain  made.  The 
reliability  of  the  measure  in  St.  Paul  seems  a  little  greater  than  in  any 
of  the  other  systems  considered.  The  progress  from  age  to  age  is  un- 
equal. From  ages  10  to  11  it  is  1.18;  from  ages  11  to  12  it  is  .83 ;  and 
from  ages  12  to  13  it  is  1.10. 

Chart  I  shows  the  progress  for  the  different  systems  both  relatively 
and  absolutely.  It  is  significant  that  while  the  progress  in  the  Madison 
County  schools  having  a  9-month  school  term  is  relatively  a  little 
greater  than  the  progress  in  the  city  schools  presented,  the  total  result 
is  less.  In  other  words,  although  the  children  gain  as  much  or  a  little 
more  in  ability  to  complete  sentences  between  the  ages  of  10  and  13, 
they  have  less  of  this  ability  when  they  began  and  less  when  they  get 


30         Study  of  Achievement  in  Country  and  Town  Schools 

through.     This  would  seem  to  indicate  either  later  entrance  in  school 
or  poorer  work  with  the  lower  grades,  possibly  both. 

The  following  table  summarizes  the  total  gain  in  ability  to  complete 
sentences,  as  measured  by  the  Trabue  Language  Scale  B,  between  the 
ages  of  10  and  13,  for  the  respective  school  systems  considered.  It 
also  shows  the  P.E.  of  this  total  gain,  and  the  number  of  cases  on 
which  this  measure  of  gain  is  based. 


School  Systems 

Total 

GAIN 

P.E.  OF 

TOTAL 

GAIN 

Total 
frequencies 

10  to  13 

10  and  13 

Madison  County,  6-month  schools 

Madison  County,  9-month  schools 

Louisville  .           .  _       _     _           _       _ 

3.12 
4.79 
3.29 
4.27 
3.11 

.316 
.304 
.174 
.170 
.106 

252 
233 
563 

Paterson 

455 

St.  Paul        -       --   - 

870 

It  should  be  noted  that  the  reliability  of  the  gains  given,  as  indicated 
by  a  relatively  small  P.E.,  is  much  greater  in  the  city  schools  than  in 
the  Madison  County  schools.  This  is  due  in  part  to  the  greater  num- 
ber of  cases.  That  it  is  not  wholly  due  to  this  cause  is  indicated  by 
the  fact  that  the  reliability  is  greater  for  the  Madison  County  9-month 
schools  than  for  the  6-month  schools,  though  the  number  of  cases  is 
slightly  less.  It  is  possible  that  this  greater  reliability  is  due  in  part 
to  a  more  uniform  type  of  work  in  the  city  and  town  school  systems 
than  in  the  country  schools. 

It  is  also  to  be  noted  that  the  combination  of  elimination,  natural 
development  and  schooling  over  a  three-year  period  increased  the  ability 
to  complete  sentences  4.79  steps  in  places  in  Madison  County  having 
a  9-month  school  term,  4.27  steps  in  Paterson,  3.29  steps  in  Louisville, 
3.12  steps  in  places  in  Madison  County  having  a  6-month  school  term, 
and  3.H  steps  in  St.  Paul.  If  it  may  be  assumed  that  the  amount  of 
this  increase  due  to  natural  development  is  the  same  in  all  these  places, 
the  efificiency  of  the  schools  in  training  and  eliminating  children  be- 
tween the  ages  of  10  and  13  in  such  ability  in  language  as  is  measured 
by  the  Trabue  Language  Scales  would  rank  in  the  above  order. 

This  ranking  does  not  agree  with  that  obtained  by  ranking  in  order 
of  the  median  ability  of  the  13-year-old  children.  Ranking  in  this 
way,  Louisville  comes  first  with  a  median  of  14.61,  St.  Paul  second 
with  13.34,  Paterson  third  with  13.30,  Madison  County  9-month  schools 
fourth  with  12.21,  and  Madison  County  6-month  schools  last  with  9.75. 


Achievement  Measured  by  Trabtie  Language  Scale 


31 


This  discrepancy  may  be  due  to  a  difference  in  the  work  with  chil- 
dren under  10,  to  a  greater  irregularity  of  attendance  of  the  younger 
children  in  some  systems  than  in  others,  to  a  difference  in  the  amount 
of  gain  due  to  natural  development  because  of  different  environment, 
to  a  difference  in  care  in  scoring  papers,  to  a  difference  in  intellectual 
level  of  the  communities,  or  to  a  combination  of  these  causes. 

The  following  table  shows  the  yearly  gains  in  each  of  the  systems 
of  schools  studied : 


School  Systems 

Yearly  Gains 

10  to  11 

11  to  12 

12  to  13 

Madison  County,  6-month  schools  .  - 

.87 

.73 

1.58 

2.27 

1.18 

1.52 

2.97 

1.56 

.48 

.83 

.73 

Madison  County,  9-month  schools.. 

1.09 

Louisville  ...         .... 

.15 

Paterson  .. 

1.52 

St.  Paul 

1.10 

Total 

6.63 

7.36 

4.59 

This  table  seems  to  indicate  that  the  greatest  gain  is  made  from 
ages  11  to  12,  but  that  material  gain  may  be  made  during  any  of  the 
yearly  periods  from  ages  10  to  13  inclusive. 


CONCLUSIONS 

1.  The  difference  in  performance  as  measured  by  the  Trabue  Lan- 
guage Scale  B  of  school  children  of  different  ages  can  be  obtained. 

2.  Since  this  test  measures  a  quality  not  proved  to  be  solely,  or  even 
largely,  determined  by  school  training,  this  difference  is  not  a  reliable 
measure  of  school  efficiency. 

3.  This  difference  does  measure  the  improvement  of  children  in  the 
respective  systems  as  to  the  function  measured,  such  improvement  be- 
ing due  to  school  training  and  other  influences. 

4.  The  children  in  the  Madison  County  6-month  schools  show  less 
improvement  during  the  three-year  period  from  10  to  13  inclusive  than 
do  the  children  in  any  of  the  other  systems  except  St.  Paul. 

5.  The  13-year-oId  children  in  the  Madison  County  6-month  schools 
show  less  ability  in  the  function  measured  than  do  the  children  of  like 
age  in  any  of  the  other  systems  studied. 

6.  The  children  in  the  Madison  County  9-month  schools  show  rea- 
sonable improvement  during  the  three-year  period  from  10  to  13  in- 


32         Study  of  Achievement  in  Country  and  Town  Schools 

elusive,  but  the  ability  of  the  13-year-old  children  to  complete  sen- 
tences is  less  than  the  like  ability  of  13-year-old  children  in  any  of  the 
systems  studied  except  the  6-month  schools  in  the  same  county. 


CHAPTER  IV 

ACHIEVEMENT  AS  MEASURED  BY  THE  COURTIS   STANDARD 
RESEARCH  TESTS  IN  ARITHMETIC  SERIES  B 


At  the  same  time  that  the  Trabue  Language  Scale  B  was  given  in 
the  schools  of  Madison  County,  the  Courtis  Standard  Research  Test 
in  Arithmetic  Series  B  was  used. 

The  problems  involved  in  finding  the  difference  in  performance  of 
different  age-groups  are  practically  the  same  as  in  the  work  with  the 
Trabue  Language  Scale  B.  Distributions  for  the  respective  age- 
groups  are  completed  on  the  same  assumptions,  and  the  same  age- 
groups  are  used  throughout.  The  number  of  examples  correctly  com- 
pleted has  been  used  as  the  score. 

The  work  in  addition,  subtraction,  multiplication  and  division  is 
presented  in  sections  1,  2,  3  and  4  respectively  of  this  chapter. 

Section  L    Addition 
Table  VII  gives  the  data  in  addition  for  the  children  10  to  13  years 
of  age  inclusive  in  the  Madison  County  schools  having  a  6-month  term. 
A  new  problem  is  presented  in  this  table  in  that  the  medians  of  the 

TABLE  VII 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Addition  Rights  in  the  6-Month  White  Schools  of  Madison  County,  Ky. 


Scores 

Age 

Total 

XI 

X2 

0 

65 
54 
62 
45 

1 

2 

3 

4 

5 

6 

7 

8 

9 

X9 

XIO 

Xll 

10 

11 
5 
3 

2 

19 
11 
5 
3 

25 
20 
19 
16 

9 
12 
19 
13 

7 

10 
5 
8 

6 
6 
7 
11 

1 
2 
4 

1 

144 

11 

4 
8 
5 

2 
4 
13 

126 

12 

2 

2 
4 

140 

13 

1 

2 

123 

P.  E. true 

Median 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.  E. 

10 

.64 

.07 

1.52 

.09 

.71 

Mil— M10=  .23 

.072 

11 

.87 

.11 

2.37 

.28 

1.04 

M12— Mll=  .13 

.092 

12 

1.00 

.12 

2.48 

.43 

1.20 

M13— M12=  .71 

.147 

13 

1.71 

.21 

4.47 

.57 

1.90 

M13— M10=1.07 

.136 

10-  and  11-year-old  groups  fall  in  the  0  to  1  interval,  and  that  the  25 
percentiles  of  all  age-groups  fall  in  the  same  interval.      It  may  be 

33 


34  Study  of  Achievement  in  Country  and  Tozvn  Schools 


questioned  whether  the  children  in  grades  1  and  2,  grouped  under 
the  captions  XI  and  X2,  should  be  considered  as  having  a  score  of  0, 
or  whether  an  attempt  should  be  made  to  distribute  their  scores.  Tab- 
ulation of  the  pupils'  test  papers  shows  that  there  are  147  children  in 
grade  3,  and  that  127  of  these  grade  3  children  made  a  score  of  0. 
Since  127  out  of  147  children  made  a  score  of  0  and  since  it  may  be 
safely  assumed  that  children  in  grades  1  and  2  would  not  do  so  well 
as  children  in  grade  3,  the  score  of  these  first  and  second  grade  chil- 
dren has  been  considered  as  0.  Scores  given  under  the  caption  0  have 
been  considered  as  distributed  evenly  between  0  and  1. 

The  large  number  of  scores  in  the  0  to  1  interval  as  well  as  the 
scores  considered  as  0  indicate  that  the  ability  in  addition  required  to 
do  any  of  the  examples  in  the  Courtis  Standard  Research  Tests  in 
Arithmetic  Series  B  is  so  great  as  to  preclude  measurement  of  many 
of  the  individuals  tested  further  than  to  show  that  their  ability  is  less 
than  the  lowest  ability  measured  by  this  test.  The  great  number  of  0 
cases  also  reduces  Q. 

TABLE  VIII 
Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Addition  Rights  in  the  9-Month  White  Schools  of  Madison  County,  Ky. 


Scores 

Total 

XI 

X2 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

X9 

XIO 

Xll 

10 

9 

1 
3 
4 

16 
9 
1 
3 

23 
21 
21 

7 

14 
13 
19 
15 

19 
12 
15 
11 

11 

7 
24 
11 

16 
10 
17 
17 

6 

7 
6 

8 

5 
9 
13 
5 

5 
2 
6 
3 



1 

1 
3 
1 
1 

127 

11 

i 
1 

8 

94 

12 

1 
1 

1 
1 

131 

13 

1 

98 

Median 

P.  E.  true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

2.07 
2.25 
3.27 
3.81 

.21 
.26 
.19 
.25 

4.20 
4.75 

4.89 
5.68 

.26 

.64 

1.40 

1.70 

1.97 
2.05 
1.74 
1.99 

Mil— M10=  .18 
M12— Mll  =  1.02 
M13— M12=  .54 
M13— M10  =  1.74 

.206 
.194 
.186 
.198 

The  total  gain  in  ability  to  add  for  the  three-year  period  from  ages 

10  to  13,  as  measured  by  the  difference  in  the  median  scores  of  the 
10-year-old  and  the  13-year-old  children  who  took  the  test,  is  1.07, 
with  a  P.E.  of  .136.  This  P.E.  is  slightly  over  12  per  cent  of  the  total 
gain  indicated. 

The  improvement  in  ability  to  add  from  year  to  year,  as  measured 
by  the  difference  between  the  median  scores  of  the  respective  age- 
groups,  is  uneven,  as  it  is  in  the  case  of  language.     From  ages  10  to 

11  the  improvement  is  .23 ;  from  ages  11  to  12  it  is  .13 ;  and  from  ages 


Achievement  Measured  by  Courtis  Arithmetic  Tests 


35 


12  to  13  it  is  .71.  The  improvement  from  ages  12  to  13  is  practically 
twice  as  great  as  the  combined  improvement  from  ages  10  to  11  and 
from  ages  11  to  12.  Apparently  the  first  real  teaching  of  such  ability 
to  add  as  is  measured  by  the  Courtis  Standard  Research  Tests  in  Arith- 
metic Series  B  in  these  schools  is  to  children  between  the  ages  of  12 
and  13. 

Table  VIII  presents  the  facts  in  regard  to  addition  in  the  9-month 
schools  of  Madison  County.  The  same  statistical  method  is  used  as 
that  used  with  the  data  from  the  6-month  schools. 

The  total  improvement  in  ability  to  add  in  these  schools  for  the 
three-year  period  from  ages  10  to  13  inclusive  is  1.74.  The  P.E.  of  this 
improvement  is  .198,  or  slightly  under  12  per  cent  of  the  total  gain. 
The  accuracy  of  the  measurement  for  the  6-month  schools  is  indi- 
cated by  a  P.E.  showing  slightly  over  12  per  cent  of  the  total  gain ; 
just  about  the  same  degree  of  reliability. 

The  improvement  by  years  varies  for  these  schools  as  it  does  for 

TABLE  IX 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Addition  Rights  in  Louisville,  Ky.   (White  Schools) 


Age 

Scores 

Total 

10 

XI 

8 
5 

X2 

16 
8 
5 

X3 

43 
16 

8 
5 

0 

12 
10 
6 

8 

1 

16 
11 
10 
9 

2 

19 
21 

22 
19 

3 

38 
28 
23 
18 

4 

33 
31 
25 
25 

5 

27 
35 
34 
29 

6 

28 
29 
26 
26 

7 

14 

28 
28 
30 

8 

18 
27 
37 
24 

9  1 

10 
21  1 
28  1 
25  1 

0  11 

5    6 
0  W 
3  13 
8  13 

12 

1 
4 
6 
13 

13 

1 
2 
9 
9 

14 

3 
4 
1 

15 

1 

"2 
4 

16 

"3 
2 

2 

17 

1 

1 
1 
1 

18 

19 

20 

21 

22 

23 

X9 

289 

11 

1 

304 

12 

1 

1 
1 

"25 

304 

13 

1 

306 

Median 

P.  E. true 
— obtained 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 

12 
13 

3.77 
5.62 
6.73 
7.46 

.21 
.18 
.18 

.27 

6.26 
8.22 
9.14 

12.80 

.43 
3.17 
4.08 
5.08 

2.91 
2.52 
2.53 
3.86 

Mil— M10  =  1.85 
M12— Mll  =  l.ll 
M13— M12=  .73 
M13— M10  =  3.69 

.170 
.155 
.202 
.213 

the  6-month  schools.  From  ages  10  to  11  it  is  .18;  from  ages  11  to  12 
it  is  1.02;  and  from  ages  12  to  13  it  is  .54.  The  greatest  gain  occurs 
between  the  ages  of  11  and  12.  This  occurs  a  year  earlier  than  the 
greatest  gain  in  the  case  of  the  6-month  schools. 

The  median  achievement  for  children  of  each  age  is  materially  higher 
than  is  the  case  in  the  6-month  schools.  For  the  13-year-old  children 
this  median  achievement  is  3.81  in  the  9-month  schools  as  against 
1.71  in  the  6-month  schools ;  a  difference  of  2.10  in  favor  of  the  schools 
having  the  longer  term. 


36  Study  of  Achievement  in  Country  and  Town  Schools 


For  the  purposes  of  comparison,  data  are  presented  in  Tables  IX 
to  XIII  inclusive  from  certain  other  school  systems. 

Table  IX,  for  Louisville,  Kentucky,  is  based  on  data  in  the  Psycho- 
logical Laboratory  of  the  Louisville  Board  of  Education,  and  is  for  cer- 
tain of  the  white  schools  of  the  city.  The  tests  were  given  under  the 
direction  of  the  Psychological  Laboratory  during  the  school  year  prior 
to  June,  1918. 

Table  X,  for  Louisiana,  is  based  on  tests  given  by  the  parish  super- 
visors in  thirteen  Louisiana  parishes.  The  schools  tested  were  white 
schools  selected  by  the  supervisors  as  neither  the  best  nor  the  worst 
in  their  respective  parishes.     They  range  in  size  from  one  teacher  to 

TABLE  X 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Addition  Rights  in  Certain  White  Schools  in  Louisiana 


Scores 

Age 

Total 

XI 

X2 

X3 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

X9 

XIO 

Xll 

10 

24 
13 
7 

43 
24 
13 

58 
43 
?4 

48 
47 
4,'i 

31 
38 
37 

24 

27 
51 

23 

28 
41 

12 
20 
30 

10 
16 

18 

6 
10 
11 

4 
8 
11 

1 

2 

--1 

1 

1 
1 

1 

287 

11 

1 
1 

1 
1 

280 

u 

1 

1 

299 

n 

7 

13 

50 

35 

42 

31 

28 

16 

16 

8 

6 

5 

1 

17 

1 

1 

277 

P.  E. true 

Median 

— obtained 
median 

75  per- 
centile 

25  per 
centile 

Q 

P.E. 

10 

.38 

.09 

2.46 

0.00 

1.23 

Mil— M10=  .96 

.094 

11 

1.34 

.13 

3.64 

0.00 

1.83 

M12— Mll  =  1.12 

.106 

12 

2.46 

.12 

4.20 

.68 

1.76 

M13— M12=  .33 

.114 

13 

2.79 

.15 

5.10 

.98 

2.06 

M13— M10=2.41 

.102 

TABLE  XI 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Addition  Rights  in  Arkansas  City 


Scores 

Age 

> 

Total 

XI 

X2 

X3 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

X{ 

10 

15 
8 
3 

54 
15 

8 

65 
54 
15 

54 
49 
63 

46 
33 
54 

19 
35 

37 

29 
17 
33 

14 

29 
34 

8 
10 
22 

6 
4 

8 

2 
3 
6 

312 

11 

2 
8 

259 

12 

3 

294 

13 

1 

3 

8 

34 

32 

36 

39 

37 

32 

12 

4 

6 

4 

5 

1 

254 

P.  E. true 

Median 

— obtained 
median 

75  per- 
centile 

25  per 
centile 

Q 

P.E. 

10 

.40 

.03 

1.00 

0.00 

.50 

Mll-M10=  .70 

.072 

11 

1.10 

.11 

3.01 

0.00 

1.50 

M12— M11  =  1.(J0 

.098 

12 

2.10 

.12 

4.22 

.75 

1.73 

M13— M12=1.23 

.106 

13 

3.33 

.13 

5.01 

1.64 

1.68 

M13— M10=2.93 

.082 

sixteen  teachers.     In  some  cases  only  a  limited  number  of  the  pupils 
were  tested  in  each  grade.     When  this  was  done,  the  teacher  was  asked 


Achievement  Measured  by  Courtis  Arithmetic  Tests 


17 


to  select  pupils  neither  the  brightest  nor  the  dullest.  This  manifestly 
gives  a  selection  that  is  not  accurately  representative  of  the  Louisiana 
schools ;  it  seems  likely  that  the  selection  tends  to  be  above  rather  than 
below  the  median  situation,  and  the  range  is  less  in  proportion  as  the 
teachers  and  supervisors  have  succeeded  in  avoiding  the  extreme  cases. 
Tables  XI  and  XII,  for  Arkansas  City  and  for  Salina,  are  based  on 
tabulations  made  from  papers  collected  by  the  Bureau  of  Educational 
Measurements  and  Standards  of  the  State  Normal  School  at  Emporia, 

TABLE  XII 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 
Addition  Rights  in  Salina,  Kan. 


Scores 

Total 

XI 

16 
4 
2 

X2 

20 
16 
4 

2 

X3 

43 

20 

16 

4 

0 

46 
15 
14 
13 

1 

43 
49 
24 
13 

2 

44 
42 
38 
30 

3 

44 

36 
48 
27 

4 

26 
36 
57 
40 

5 

20 
37 
43 
32 

6 

15 
11 
29 
40 

7 

14 
8 
6 

16 

8 

i2 

8 
17 

9  1 

3 

8  _ 
6 
11  1 

0  11 
1 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

X9  XIO 

10 

335 

11 

9  'i 

0    5 

1 

4 

4 

2 

....  . 
5 

"l 

296 

12 

311 

13 

1 

2 

— 

— 

274 

Median 

P.  E.  true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

1.98 
3.06 
4.16 
5.25 

.12 
.13 
.12 
.15 

3.89 
5.10 
5.70 
7.25 

.10 
1.34 
2.46 
3.24 

1.89 
1.34 
1.62 
2.00 

Mil— M10= 1.08 
M12-M11  =  1.10 
M13— M12  =  1.09 
M13— M10=3.27 

.120 
.114 
.114 
.120 

TABLE  XIII 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 
Addition  Rights  in  Hibbing,  Minn. 


Age 

Scores 

Total 

X2 
16 

X3 

34 
16 

0 

34 

23 

11 

3 

1 

27 
30 
16 
4 

2 

31 
20 

25 
8 

3 

32 
32 
16 
15 

4 

24 
25 
14 

to 

5 

19 

19 
13 

6 

12 
12 
24 
9 

7 

12 
17 
17 
16 

8 

7 
12 
19 

9 

3 
9 
Ifi 

10 

2 
9 
13 
11 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

X9 

XIO 

10 

1 
8 
4 
10 

1 
3 
7 
2 

1 
4 
3 
1 

"3 
3 
3 

1 
1 
5 
2 

257 

11 

244 

12 

2 

"2 

2 
2 

2 

4 
33 

"4 

222 

13 

—  - 

—  - 

18  11 

1 

1 

179 

Median 

P.E.  true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 

2.56 
4.00 

.16 

.21 

4.78 
7.22 

Q   34 

.41 
1.73 

3   91 

2.18 
2.74 
7.  OR 

W 

M 

11- 

12- 

13- 

-M10=1.44 
-Mll  =  2.41 
-M19  — 5  22 

.164 
.206 
.322 

13 

8.6 

3 

45 

15 

12 

5.3 

6 

4 

88 

^ 

13- 

-Ml 

0=6 

.07 

297 

38  Study  of  Achievement  in  Country  and  Town  Schools 

Kansas.  The  tests  were  given  and  scored  by  the  teachers  during  the 
two  years  prior  to  June,  1917. 

Table  XIII,  for  Hibbing,  Minnesota,  is  based  on  papers  collected  by 
the  Department  of  Research  of  the  Hibbing  schools.  The  tests  were 
given  by  the  teachers  and  scored  by  clerks  in  the  fall  of  1919. 

In  the  following  summary  the  total  improvement  in  ability  to  add 
for  the  three-year  period  from  ages  10  to  13  inclusive  is  given  for  each 
system  of  schools  reported,  and  also  the  median  ability  of  each  13-year- 
old  group.  This  median  for  the  13-year-old  group  may  be  considered 
in  a  way  as  a  measure  of  the  result  obtained  in  any  system  with  chil- 
dren up  to  the  age  of  13. 


School  Systems 


Hibbing 

Louisville 

Salina 

Arkansas  City 

Louisiana 

Madison  County,  9-month  schools 
Madison  County,  6-month  schools 


Total  gain 


10  to  13 

inclusive 


6.07 
3.69 
3.27 
2.93 
2.41 
1.74 
1.07 


Medians 


13-year-old 
children 

8.63 
7.46 
5.25 
3.33 
2.79 
3.81 
1.71 


It  is  significant  that  the  ranking  in  order  of  median  ability  of  13- 
year-old  children  so  nearly  coincides  with  ranking  in  order  of  total 
improvement  for  the  three-year  period  from  10  to  13  inclusive.  The 
only  difference  is  that  the  order  of  Louisiana  schools  and  the  Madison 
County  9-month  schools  is  inverted  in  the  two  rankings.  The  ability 
to  add  is  a  mechanical  ability,  taught  definitely  in  the  schools,  and  very 
little  affected  by  the  process  of  natural  development  which  was  so 
potent  a  factor  in  the  case  of  language  ability  as  measured  by  the  Tra- 
bue  Language  Scale. 

Differences  in  method  of  giving  the  tests  and  in  detail  of  procedure 
in  different  places  affect  the  medians  of  the  13-year-old  groups  of  chil- 
dren. These  elements  of  error  may  be  of  determining  size  in  cases 
where  the  tests  are  given  by  interested  parties,  such  as  teachers.  When 
the  difference  between  medians  for  groups  of  children  of  different 
ages  is  taken  as  a  measure,  the  sources  of  error  referred  to  above 
neutralize  each  other,  since  it  may  be  assumed  that  the  errors  will  be 
as  great  for  one  group  of  children  as  for  another  group,  the  tests  be- 
ing given  at  the  same  time  in  the  same  system  and  with  the  same 


Achievement  Measured  by  Courtis  Arithmetic  Tests 


39 


general  directions  or  lack  of  directions.  The  ranking  in  order  of  the 
total  gain  in  ability  to  add  over  the  three-year  period  from  ages  10  to 
13  inclusive  is  therefore  the  more  significant  ranking. 

The  following  summary  shows  the  yearly  gain  in  each  of  the  sys- 
tems of  schools  studied : 


School  Systems 


Hibbing 

Louisville 

Salina 

Arkansas  City 

Louisiana 

Madison  County,  9-month  schools 
Madison  County,  6-month  schools 

Total 


Yearly  Gains 


10  to  11 

1.44 
1.85 
1.08 
.70 
.96 
.18 
.23 


6.44 


11  to  12 


2.41 
1.11 
1.10 
1.00 
1.12 
1.02 
.13 


7.89 


12  to  13 


2.22 
.73 
1.19 
1.23 
.33 
.54 
.71 


6.95 


The  extreme  variation  in  the  amount  of  yearly  gain  is  significant 
in  that  it  shows  so  great  a  lack  of  uniformity  in  the  time  of  teaching 
so  fundamental  a  process  as  that  of  column  addition.  The  totals  in- 
dicate that  as  a  rule  greater  progress  is  made  in  teaching  this  process 
between  the  ages  of  11  and  12;  that  the  period  from  ages  12  to  13  is 
next;  and  that  the  least  gain  is  made  from  ages  10  to  11. 


CONCLUSIONS 

1.  Such  diflFerence  in  performance  in  addition  as  is  measured  by 
the  Courtis  Standard  Research  Tests  can  be  obtained  for  school  chil- 
dren of  different  ages. 

2.  Since  this  test  measures  an  ability  trained  in  the  schools  and  not 
greatly  dependent  on  natural  development,  this  difference  in  perform- 
ance is  a  valid  measure  of  school  efficiency  in  teaching  this  process. 

3.  Material  gain  in  ability  to  add  may  be  made  with  children  dur- 
ing any  of  the  age  periods,  10  to  11,  11  to  12,  or  12  to  13. 

4.  The  difference  in  ability  of  children  of  different  age-groups  is  a 
valid  measure,  even  though  there  may  have  been  some  irregularity  in 
the  giving  of  the  tests. 

5.  That  all  the  school  systems  investigated  are  doing  better  work  in 
the  teaching  of  addition  than  are  the  schools  of  Madison  County. 


40         Study  of  Achievement  in  Country  and  Town  Schools 

6.  That  the  schools  in  Madison  County  having  a  6-month  school 
term  are  doing  poorer  work  than  the  schools  having  a  9-month  term. 
That  is  to  say,  the  one-  and  two-teacher  schools  are  doing  poorer  work 
than  the  larger  schools. 

Section  2.     Subtraction 

The  data  presented  in  subtraction  are  tabulated  from  the  same  sets 
of  papers  used  for  addition.  The  subtraction  tests  were  given  under 
the  same  conditions  as  those  in  addition,  by  the  same  people,  and  were 
corrected  and  collected  in  the  same  way.  The  statistical  procedure 
has  been  the  same  in  tabulating  and  calculating. 

Table  XIV  gives  the  facts  in  regard  to  subtraction  in  the  Madison 
County  6-month  schools. 

TABLE  XIV 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Subtraction  Rights  in  the  6-Month  White  Schools 

of  Madison  County,  Ky. 


Scores 

Age 

XI 

X2 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

X9 

XIO 

XU 

Tota 

10 
11 
12 
13 

10 
6 
3 
2 

19 
10 
6 
3 

76 
69 
61 
48 

13 
11 
13 
12 

7 
6 

13 
11 

5 
6 
10 

8 

8 
8 
8 
8 

2 
3 

7 
5 

1 

"'"3 
4 

141 

3 
4 

2 

1 

2 
4 
11 

125 

2 

1 

2 

2 
4 

..... 

137 

1 

123 

Median 

P.  E.  true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

.54 

.67 

.97 

1.70 

.05 
.08 
.17 
.25 

1.05 
1.79 
3.67 
5.05 

.08 
.22 
.41 
.53 

.48 

.78 

1.63 

2.26 

Mil— M10=   .13 
M12— Mll=   .30 
M13— M12=  .73 
M13— M10=1.16 

.058 
.111 
.188 
.162 

In  these  schools  the  median  ability  in  subtraction  for  children  10, 
11  and  12  years  of  age  is  between  0  and  1,  and  the  25  percentile  for 
each  of  the  age-groups  presented  falls  within  the  same  interval.  Ap- 
parently most  of  the  children  in  these  schools  under  14  years  of  age 
possess  an  ability  in  subtraction  that  is  so  slight  that  it  cannot  be 
measured  by  this  test. 

The  total  gain  in  ability  to  subtract  for  the  three-year  period  from  ages 
10  to  13  inclusive,  as  measured  by  the  difference  between  the  median 
scores  of  the  10-year-old  children  and  the  13-year-old  children,  is  1.16. 
The  P.E.  of  this  measure  of  gain  from  the  true  measure  is  .162,  almost 
14  per  cent  of  the  total  gain.  The  probable  actual  deviation  from  the 
difference  obtained  is  reasonably  small,  but  the  very  small  difference 


Achievement  Measured  by  Courtis  Arithmetic  Tests 


41 


obtained  makes  this  probable  deviation  quite  large  proportionately. 
The  same  thing  is  true  in  the  case  of  addition. 

The  improvement  from  year  to  year  increases  consistently.  From 
ages  10  to  11  it  is  .13 ;  from  ages  11  to  12  it  is  .20;  and  from  ages  12  to 
13  it  is  .73. 

Table  XV  gives  the  facts  in  regard  to  subtraction  in  the  Madison 
County  9-month  schools. 

The  median  ability  in  subtraction  of  each  of  the  age-groups  is  above 
1.  The  25  percentiles  of  the  10-  and  11-year-old  groups  fall  in  the 
0  to  1  interval. 

TABLE  XV 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Subtraction  Rights  in  the  9-Month  White  Schools 

OF  Madison  County,  Ky. 


Scores 

Age 

Total 

XI 

X2 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

X9 

XIO 

XI 1 

10 

9 

? 

17 

38 

12 

6 

5 

6 
6 

17 
6 

11 

9 

7 
5 

5 

3 
6 

1  -... 
1        4 

2 

124 

11 

1 

98 

12 

3 

2 

25 

8 

6 

16 

10 

13 

14 

10 

7 

9       3 

1 

1 

1 

1 

130 

13 

4 

3 

3 

8 

13 

U 

7 

9 

9 

6 

10 

4        4 

1 

1 

--- 

8 

1 

1 

103 

P.  E.  true 

Medis 

in 

— obtained 
median 

75  pe 
eentil 

r- 
e 

25  per- 
centile 

Q 

P.E. 

10 

1.66 

.26 

4.8S 

.17 

2.35 

Mil— M10=  .34 

.270 

11 

2.  DC 

.33 

5.83 

.51 

2.66 

M12— Mll  =  2.50 

.280 

12 

4.5C 

.31 

7.05 

1.31 

2.87 

M13— M12=  .77 

.289 

13 

5.27 

.35 

8.4: 

2.59 

2.91 

M13— M10=3.61 

.279 

The  total  gain  for  the  three-year  period  from  ages  10  to  13  inclusive 
is  3.61,  as  against  a  gain  for  a  similar  period  of  years  in  the  6-month 
schools  of  1.16.  The  P.E.  of  the  gain  in  the  9-month  schools  (3.61) 
is  .279;  a  little  less  than  8  per  cent  of  the  total  gain.  The  probable 
actual  deviation  of  the  true  from  the  obtained  difference  in  the  case 
of  the  9-month  schools  is  greater  than  in  the  case  of  the  6-month 
schools,  .279  as  against  .162,  but  in  proportion  to  the  respective  gains 
it  is  less. 

The  progress  from  year  to  year  is  uneven.  From  ages  10  to  11  it  is 
.34;  from  ages  11  to  12  it  is  2.50;  and  from  ages  12  to  13  it  is  .77. 
By  far  the  largest  gain  occurs  between  the  ages  11  and  12. 

Tables  XVI  to  XX  inclusive  present  comparative  data  from  other 
school  systems,  as  was  done  for  addition.  In  the  following  summarj^ 
the  total  improvement  in  ability  to  subtract  for  the  three-year  period 
from  ages  10  to  13  inclusive  is  given  for  each  of  the  systems  of  schools 


42         Study  of  Achievement  in  Country  and  Town  Schools 


TABLE  XVI 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Subtraction  Rights  in  Certain  White  Schools  of  Louisville,  Ky. 


Aire 

Scores 

Total 

XI 

10 
5 

X2 

18 
10 
5 

X3 

45 
18 
10 
5 

0 

5 
9 
2 
3 

1 

15 

11 

6 

1 

2 

22 

12 

15 

1 

3 

29 
18 
12 
2 

4 

34 
22 
20 
15 

5 

27 
27 
28 
26 

6 

27 
32 
31 
20 

7 

14 

37 
36 

8 

18 
31 
34 

29 

9 

11 
31 
23 
31 

10 

4 
21 

2e 

21 

11 

4 
10 
19 
30 

12 

2 
12 
11 
16 

13 

1 

3 
11 
11 

14  15  16 

..    1    1 
5    1    1 
10    9    3 
13    5    7 

17 

18 

19 

20 

21 

22 

23 

24 

X9 

10 

11 

12 

286 

1 
2 
2 

1 
5 
3 

"2 
2 

1 
2 
2 

"2 

1 

1 

313 

324 

1 

26 

310 

1 

Median 

P.  E.  true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

u 

12 
13 

4.02 
6.76 
7.89 
9.54 

.23 
.19 
.18 
.20 

6.42 
9.31 
10.76 
12.78 

.10 
3.73 
5.39 
7.12 

3.16 
2.79 
2.68 
2.83 

M11-M10=2.74 
M12— Mll  =  1.13 
M13— M12  =  1.65 
M13— M10  =  5.52 

.184 
.162 
.162 

.184 

TABLE  XVII 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 
Subtraction  Rights  in  Certain  Schools  in  Louisiana 


Scores 

Total 

XI 

24 
14 

7 

X2 

46 
24 
14 

7 

X3 

52 
46 
24 
14 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15     X9 

XIO 

Xll 

10 
11 

12 
13 

52 
46 
42 
36 

21 
35 
23 
18 

38 
30 
28 
29 

13 

22 
36 
29 

15 
21 
35 
34 

10 
19 
29 
21 

10 
12 
20 
25 

1 
6 

K 

3 
4 
11 
12 

1 
5 
9 
12 

297 

1 
8 
6 

1 
6 
3 

2 
.... 

1 

1 

.... 

289 

--- 

1 

1       1 
_-..      16 

304 

277 

Median 

P.  E.  true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

.31 
1.41 
3.38 
4.16 

.13 
.14 
.17 
.19 

3.75 
3.98 
5.65 
6.79 

0.00 

0.00 

.73 

1.68 

1.87 
1.99 
2.41 
2.55 

Mil— M10=1.10 
M12— Mll  =  1.97 
M13— M12=  .78 
M13— M12=3.85 

.120 
.134 
.156 
.144 

TABLE  XVIII 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Subtraction  Rights  in  Arkansas  City 


Age 

Scores 

Total 

XI 

"18 
8 
4 
1 

X2 

52 
18 
8 
4 

X3 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

X9 

10 
11 
12 
13 

60 

52 

18 

8 

37 
33 
29 
21 

31 
31 
22 
10 

25 
22 
31 
18 

25 
24 
26 
25 

23 
16 
45 
31 

16 
18 
25 
20 

7 

7 

25 

37 

8 

17 
19 
26 

""■3 
16 

25 

1 

1 

7 

11 

"2 
2 

7 

2 
5 
3 
3 

305 

257 

2 
4 

"2 

1 

.... 

283 
254 

Median 

P.  E. true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 

12 
13 

.60 
1.56 
4.07 
5.45 

.11 
.16 
.17 
.17 

3.23 
4.29 
6.17 
7.59 

0.00 
0.00 
1.53 
3.06 

1.61 

2.14 
2.32 
2.26 

Mil— M10=  .96 

M12— Mll=2.51 
M13— M12=1.38 
M13-M10=4.85 

.122 
.141 
.148 
.130 

Achievement  Measured  by  Courtis  Arithmetic  Tests 


43 


TABLE  XIX 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 
Subtraction  Rights  in  Salina,  Kan. 


Age 

Scores 

Total 

XI 

15 

X2 
19 

X3 
46 

0 
17 

1 

21 

2 

3 
30 

4 
41 

5 
35 

6 
31 

7 
23 

8 
20 

9 
6 

10 
4 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

X9 

XIO 

10 

341 

11 

4 
3 

15 
4 
3 

19 
15 
4 

11 
3 
5 

19 
5 
3 

13 
10 

4 

14 

27 
8 

40 
36 
17 

32 
27 
31 

36 
45 
45 

23 
28 
37 

30 
33 

28 

18 
27 
20 

8 
19 
24 

7 
11 
13 

4 
8 
6 

2 
3 

7 

295 

1?, 

i 

3 
3 

1 

1 

1 

2 
1 

"2 

309 

13 

- 

2 

1 

266 

.     P.  E.  true 

Median 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

3.65 

.19 

5.96 

.30 

2.83 

Mil— M10=  1.74 

.162 

11 

5.39 

.19 

7.79 

2.44 

2.62 

M12— Mll  =  1.15 

.148 

12 

6.54 

.16 

8.87 

4.28 

2.29 

M13— M12=  .81 

.134 

13 

7.35 

.15 

9.72 

5.72 

2.00 

M13— M10=3.70 

.150 

TABLE  XX 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Subtraction  Rights  in  Hibbing,  Minn. 


Scores 

Age 

Total 

X2 
16 

X3 

35 
16 

0 

33 
20 
3 

1 

9 
6 

6 

2 

10 
11 

6 

3 

12 
9 
13 

4 

14 
25 
11 

5 

22 
15 

6 

20  1 
20  1 

V  1 

7    8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

X9 

XI 

10 

6  16 
6  22 
9  18 

15 
18 

18 

4 
19 
19 

9 
12 

?5 

6 
6 
11 

5 

7 

7 

3 
4 
13 

"2 

3 
4 

7 

248 

11 

2 

? 

1 
3 

2 

1 

238 

1?, 

1 

1 

4 

227 

13 

2 

2 

4 

4 

10 

9 

3 

9  16 

13 

10 

19 

15 

5 

7 

6 

1 

4 

2 

— 

1 

32 

4 

179 

P.  E.  true 

Median 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

4.64 

.30 

7.93 

.33 

3.80 

Mil— M10=2.16 

.240 

11 

6.80 

.25 

10.02 

3.72 

3.15 

M12— Mll=2.39 

.212 

12 

9.19 

.23 

11.93 

6.26 

2.83 

M13— M12=2.15 

.260 

13 

11.34 

.36 

15.87 

8.10 

3.88 

M13— M10  =  6.70 

.284 

reported,  and  also  the  median  ability  of  each  13-year-old  group.  As 
in  addition,  so  in  subtraction,  this  median  for  the  13-year-old  group 
may  be  considered  in  a  way  as  a  measure  of  the  result  obtained  in 
any  system  with  children  up  to  the  age  of  13. 


School  Systems 


Hibbing 

Louisville 

Arkansas  City 

Louisiana 

Salina 

Madison  County,  9-month  schools 
Madison  County,  6-month  schools 


Total  gain 


10  to  13 
inclusive 


6.70 
5.52 
4.85 
3.85 
3.70 
3.61 
1.16 


Medians 


13-year-old 
children 


11.34 
9.54 
5.45 
4.16 
7.35 
5.27 
1.70 


44         Study  of  Achievement  in  Country  and  Tozvn  Schools 

The  ranking  in  order  of  total  gain  made  for  the  three-year  period 
from  ages  10  to  13  inclusive  corresponds  quite  well  with  the  ranking 
in  order  of  medians  for  the  13-year-old  children.  This  correspond- 
ence is  not  so  close  as  was  the  case  with  addition ;  there  are  four  dis- 
placements in  the  ranking.  As  was  the  case  with  addition,  the  rank- 
ing in  order  of  total  gain  for  the  three-year  period  is  the  more  sig- 
nificant, since  the  use  of  a  difference  as  a  measure  tends  to  neutralize 
errors  in  the  giving  and  scoring  of  the  test. 

It  is  interesting  to  note  that  the  rank  in  gain  in  ability  to  subtract  is 
not  the  same  as  that  in  ability  to  add.  Arkansas  City  and  Louisiana 
both  come  ahead  of  Salina  in  subtraction,  and  not  in  addition.  This 
difference  between  the  rank  of  these  systems  for  the  two  processes 
would  seem  to  indicate  that  subtraction  needs  to  be  taught ;  that  im- 
provement in  addition  does  not  necessarily  carry  with  it  exactly  pro- 
portionate ability  to  subtract. 

The  following  summary  shows  the  gain  for  each  yearly  age-period 
in  the  systems  studied : 


School  Systems 


Hibbing 

Louisville 

Arkansas  City 

Louisiana 

Salina 

Madison  County,  9-month  schools 
Madison  County,  6-month  schools 

Total 


10  to  11 


2.21 

2.74 

.96 

1.10 

1.74 

.34 

.13 


9.22 


Yearly  Gains 


11  to  12 


2.34 
1.13 
2.51 
1.97 
1.15 
2.50 
.30 


11.90 


12  to  13 


2.15 
1.65 
1.38 

.78 
.81 
.77 
.73 


8.27 


The  variations  are  as  great  in  the  amount  of  yearly  gain  as  they 
were  shown  to  be  in  addition.  As  in  addition,  so  in  subtraction,  the 
greatest  yearly  gain  seems  to  be  between  the  ages  of  11  and  12.  In 
subtraction  the  next  greatest  gain  seems  to  be  between  the  ages  of  10 
and  11,  while  in  the  case  of  addition  the  second  greatest  gain  was  be- 
tween the  ages  of  12  and  13.  The  smallest  gain  is  made  between  the 
ages  of  12  and  13. 

CONCLUSIONS 

1.  The  conclusions  reached  in  regard  to  addition  (p.  39)  hold  in  the 
case  of  subtraction. 


Achievement  Measured  by  Courtis  Arithmetic  Tests 


45 


2.  Improvement  in  addition  does  not  necessarily  carry  with  it  pro- 
portionate ability  to  subtract. 

Section  3.     Multiplication 

The  data  presented  in  multiplication  are  from  the  same  sources  as 
those  for  addition  and  subtraction,  and  the  method  of  treatment  has 
been  the  same  throughout. 

Table  XXI  gives  the  facts  in  regard  to  multiplication  in  the  Madison 
County  6-month  schools. 

TABLE  XXI 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Multiplication  Rights  in  the  6-Month  White  Schools 

OF  Madison  County,  Ky. 


Scores 

Age 

Total 

XI 

X2 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

X9 

XIO 

Xll 

in 

9 
8 
4 
2 

19 
9 
6 
4 

82 
75 
62 
57 

16 
11 
12 
15 

3 
11 
16 

8 

5 

8 
12 
9 

4 
2 

9 
5 

1 
2 
3 
3 

1 

140 

11 

2 
4 
10 

'"2 
4 

—  - 

124 

}?. 

4 

1 
1 

1 

136 

13 

4 

—  - 

-  — 

124 

P.  E. true 

Median 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

.51 

.04 

.93 

.08 

.42 

Mil— M10=.ll 

.036 

11 

.62 

.05 

1.27 

.21 

.53 

M12— Mll  =  .31 

.094 

12 

.93 

.14 

3.16 

.38 

1.39 

M13— M12  =  .05 

.142 

13 

.98 

.18 

3.77 

.43 

1.67 

M13— M10=.47 

.111 

The  median  of  each  of  the  age-groups  given  falls  below  1,  and  even 
the  75  percentile  of  the  10-year-old  group  falls  between  0  and  1.  It 
seems  that  most  of  the  children  in  these  schools  below  the  age  of  14 
have  an  ability  in  multiplication  that  is  less  than  can  be  measured  by 
the  Courtis  Standard  Research  Tests  in  Arithmetic  Series  B. 

The  total  gain  in  ability  to  multiply  during  the  three-year  period,  ages 
10  to  13  inclusive,  is  only  .47.  The  P.E.  of  this  statement  of  gain  is 
.111,  something  over  25  per  cent  of  the  gain  itself.  The  gain  noted  is 
very  slight.  Apparently  these  6-month  schools  in  Madison  County  are 
failing  to  teach  most  of  the  pupils  under  14  how  to  multiply. 

The  improvement  from  year  to  year  necessarily  is  very  slight,  since 
the  total  improvement  is  so  small.  From  ages  10  to  11  the  improve- 
ment is  .11 ;  from  ages  11  to  12  it  is  .31 ;  and  from  ages  12  to  13  it  is 
.05.     The  greatest  gain  in  any  one-year  period  is  .31  from  ages  11  to  12. 

The  results  of  instruction  in  multiplication  in  these  schools  are  very 
meager. 


46         Study  of  Achievement  in  Country  and  Tozvn  Schools 


TABLE  XXII 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Multiplication  Rights  in  the  9-Month  White  Schools 

OF  Madison  County,  Ky. 


SconE3 

Age 

, 

Total 

XI 

X2 

0 

1 

2 

$       4 

5 

6 

7 

8 

9 

10 

11 

X9 

XIO 

Xll 

in 

9 
1 

3 

16 
9 
1 

37 
31 
32 

4 

10 
14 

12 
7 
14 

4      10 
7      12 
>3      16 

12 
11 
10 

6 
4 
9 

120 

11 

3 

""2 

1 
1 

96 

12 

3 

2 

i 

131 

i:h 

4 

3 

13 

10 

11 

1        9 

12 

11 

5 

2 

8 

1 

1 

101 

P.  E. true 

Median 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

.94 

.21 

3.85 

.13 

1.86 

Mil— M10  = 

.76 

.206 

11 

1.70 

.26   ^ 

4.58 

.45 

2.06 

M12— Mll  = 

1.36 

.200 

12 

3.06 

.20 

4.56 

.87 

1.84 

M13-M12  = 

.80 

.216 

13 

3.86 

.29 

6.25 

1.52 

2.36 

M13— M10  = 

2.92 

.222 

Table  XXII  gives  the  facts  in  regard  to  multiplication  in  the  9- 
month  schools  of  Madison  County. 

The  median  ability  in  multiplication  in  these  schools  for  10-year-old 
children  is  .94;  a  little  less  than  1.  The  25  percentile  of  the  10-,  11- 
and  12-year-old  groups  is  less  than  1  in  each  case.  The  situation 
here  presented  is  materially  better  than  that  in  the  6-month  schools. 

The  total  gain  in  ability  to  multiply  for  the  three-year  period  from  ages 
10  to  13  inclusive  is  2.92.  The  contrast  betw^een  this  gain  and  that  in 
the  6-month  schools  (.47)  is  marked.  The  P.E.  of  this  gain  of  2.92 
is  .222,  a  little  over  7  per  cent  of  the  gain.  The  probable  actual  de- 
viation of  the  true  from  the  obtained  measure  is  greater  in  the  case  of 
the  9-month  schools  than  in  the  case  of  the  6-month  schools,  but  in 
proportion  to  the  gain  made  it  is  much  less. 

The  improvement  in  ability  to  multiply  from  ages  10  to  11  is  .76; 
from  ages  11  to  12  it  is  1.36;  and  from  ages  12  to  13  it  is  .80.  The 
gain  during  any  one  of  the  year  periods  is  much  greater  than  the  gain 
for  the  entire  three-year  period  in  the  6-month  schools.  The  great- 
est gain  is  from  ages  1 1  to  12,  as  is  the  case  in  the  6-month  schools. 

Tables  XXIII  to  XXVII  inclusive  give  comparative  data  in  regard 
to  multiplication  from  other  school  systems.  In  the  following  sum- 
mary the  total  improvement  in  ability  to  multiply  during  the  three-year 
period  from  ages  10  to  13  inclusive  is  given  for  each  of  the  school  sys- 
tems studied,  and  also  the  median  ability  for  the  respective  groups  of 
13-year-old  children.  The  schools  are  listed  in  the  order  of  amount  of 
improvement  made. 


Achievement  Measured  by  Courtis  Arithmetic  Tests 


47 


TABLE  XXIII 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Multiplication  Rights  in  Certain  White  Schools  in  Louisville,  Ky. 


Age 

Scores 

Total 

XI 

X2 

X3 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

10 

10 
5 

16 
10 

5 

43 

16 

10 

5 

7 

10 
2 
3 

15 
8 
9 
3 

23 
11 
U 
9 

34 

17 
18 
18 

32 
37 
3J 
22 

30 
41 
34 
32 

26 
36 
38 
43 

21 
35 
35 
40 

12 
32 
41 
38 

5 
21 
34 
34 

7 
14 
15 

18 

3 
3 

17 
13 

284 

11 
12 

13 

7 
9 
13 

5 
6 

8 

1 

2 
2 

309 

""4 

2 

1 

320 
305 

Median 

P.  E.  true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

3.82 
5.98 
7.05 
7.43 

.21 
.14 
.15 
.14 

6.11 
8.17 
9.17 
9.46 

.28 
4.00 
4.80 
5.50 

2.91 
2.08 
2.18 
1.98 

Mil— M10=2.16 
M12— Mil  =  1.07 
M13— M12=  .38 
M13— M10=3.61 

.158 
.127 
.120 
.152 

TABLE  XXIV 

Age  Distribution,  10  to  13  Inclusi\-e,  of  Courtis  Series  B  Arithmetic  Tests 

Multiplication  Rights  in  Certain  White  Schools  in  Louisiana 


Age 

Scores 

Total 

XI 

X2 

X3 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

X9 

XIO 

Xll 

10 

24 
13 

7 

42 
24 
13 

7 

61 

43 
24 
13 

69 
63 
74 
50 

24 
31 
36 
33 

21 
30 
28 
35 

21 
26 
34 
25 

12 
16 
34 

27 

8 
11 
21 
23 

4 
9 
12 
17 

2 
7 
5 
16 

289 

11 

4 
6 
3 

1 
3 
2 

1 

1 
1        1 

1 

1 

17 

280 

12 
13 

'"3 

--- 

i 

1 

300 

1 

275 

Median 

P.  E.  true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

.23 

.95 

1.88 

2.98 

.06 
.12 
.13 
.17 

1.85 
3.23 
4.26 
5.70 

0.00 

0.00 

.41 

.97 

.92 
1.61 
1.92 
2.86 

Mil— M10=  .72 
M12— Mll=  .93 
M13— M12=1.10 
M13— M10=2.75 

.080 
.106 
.136 
.117 

TABLE  XXV 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Multiplication  Rights  in  Arkansas  City 


Scores 

Total 

XI 

X2 

X3 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

X9 

10 

14 

8 
4 

1 

51 
14 

8 
4 

61 
51 

14 

8 

63 

41 
49 
30 

44 
21 
25 
18 

24 
40 
38 
22 

24 
22 
50 
24 

11 

21 
31 
3C 

6 
15 

22 
22 

298 

11 

9 

28 
28 

6 
16 
16 

2 

2 

24 

8 
4 
4 

258 

12 
13 

2 
3 

1 
6 

2 
4 

i 

296 
245 

Median 

P.  E. true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

.36 
1.71 
3.20 
4.51 

.06 
.14 
.15 
.19 

1.78 
3.84 
5.13 
6.88 

0.00 

0.00 

.97 

2.01 

.89 
1.92 
2.08 
2.43 

Mil— M10=  1.35 
M12— Mll=1.49 
M13— M12=1.31 
M13— M10=4.15 

.098 
.127 
.150 
.126 

48         Study  of  Achievement  in  Country  and  Town  Schools 

TABLE  XXVI 

Age  Distribution,  10  to  13  Incx-usive,  of  Courtis  Series  B  Arithmetic  Tests 

Multiplication  Rights  in  Salina,  Kan. 


Age 
10 

Scores 

Total 

XI 

16 
3 
3 

X2 

22 
16 
3 
1 

X3 

48 
22 
16 
3 

0 

31 
19 
8 
6 

1 

27 
17 

8 
8 

2 

20 
22 
U 
13 

3 

23 
23 
29 
11 

4 

48 
21 
29 
31 

5 

48 
52 
45 
27 

6 

24 
22 
51 
46 

7 

10 

8 
19 
29 

8 

9 
10 
33 
28 

9 

4 
17 
27 
19 

10 

4 
4 
19 
10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

X9 

SIO 

334 

11 

5 
19 
15 

2 
3 

7 

'7 
4 

2 
1 

8 

1 

1 

267 

12 

2 
4 

"2 

333 

13 

- 

2 

2 

275 

Median 

P.  E. true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

3.13 
4.54 
6.28 
6.81 

.18 
.18 
.16 
.20 

5.32 
6.23 
8.84 
9.18 

0.00 
1.39 
4.18 
4.86 

2.66 
2.44 
2.33 
2.66 

Mil— M10=1.41 
M12— Mll  =  1.64 
M13— M12=  .53 
M13— M10=3.68 

.155 
.148 
.156 
.162 

TABLE  XXVII 
Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 


Multiplication  Rights 

IN 

HiBBiNG,  Minn 

Age 

Scores 

Total 

X2 

X3 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

6 

17 

X9 

XIO 

10 

18 

35 
16 

34 
19 
7 
3 

23 
11 
10 
6 

29 
24 
12 

4 

35 
25 
17 
12 

20 
23 

27 
12 

21 
42 
29 
13 

16 

25 
27 
13 

12 
19 
26 
17 

9 
10 
18 
16 

5 
15 
18 
11 

4 
8 
10 
12 

1 

1 
3 
12 

1 

2 

9 

8 

261 

11 

2 
6 
3 

1 
1 

"4 

2 

1 
1 

244 

12 

1 

4 
33 

"""4 

230 

13 

181 

Median 

P.  E. true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 
11 
12 
13 

2.77 
5.09 
6.48 
8.65 

.18 
.17 
.18 
.32 

5.17 
6.92 
8.97 
12.59 

.41 
2.62 
4.42 
5.63 

2.38 
2.15 
2.27 
3.48 

Mll- 
M12- 
M13- 
M13- 

-M10=2.32 
-Mll  =  1.39 
-M12=2.17 
-M10=5.88 

.140 
.140 
.220 
.220 

As  is  the  case  in  addition  and  subtraction,  the  ranking  in  order  of 
gain  made  in  ability  for  the  three-year  period  from  ages  10  to  13  inclu- 
sive does  not  correspond  exactly  with  the  ranking  in  order  of  ability  of 


Total  gain 

Medians 

School  Systems 

10  to  13 
inclusive 

13-year-old 
children 

Hibbing                                                              -   - 

5.88 
4.15 
3.68 
3.61 
2.92 
2.75 
.47 

8.65 

Arkansas  City    .      ._     -       -             -           -- 

4.51 

Salina                                     _   .   __                       -   - 

6.81 

Louisville                                                    _  -     

7.43 

Madison  County,  9-nionth  schools            - 

3.86 

Louisiana                                                          

2.98 

Madison  County,  6-nionth  schools                       - 

.98 

Achievement  Measured  by  Courtis  Arithmetic  Tests 


49 


13-year-old  children.  The  measure  of  gain  made  is  probably  the 
more  significant  measure,  as  for  addition  and  subtraction. 

It  must  be  borne  in  mind  that  the  steps  of  improvement  are  not 
necessarily  of  equal  value.  It  may  be  more  difficult  to  teach  a  child 
who  cannot  multiply  to  multiply  well  enough  to  do  one  example  cor- 
rectly than  it  is  to  teach  a  child  who  can  do  one  example  correctly  to  do 
two  examples  correctly.  In  other  words,  because  Hibbing  makes  twice 
as  much  improvement  as  Louisiana  does  not  necessarily  mean  that  the 
teaching  in  Hibbing  is  twice  as  good  as  that  in  Louisiana.  This  dif- 
ficulty in  evaluating  the  results  of  this  test  is  not  due  to  the  fact  that 
a  difference  between  the  median  abilities  of  age-groups  is  used  as  a 
measure,  but  rather  to  the  manner  in  which  the  test  is  constructed. 
The  unit  in  which  the  result  is  stated  is  not  one  of  the  relative  diffi- 
culty with  which  those  results  are  obtained. 

The  following  summary  shows  the  gain  for  each  yearly  age  period 
in  the  systems  studied : 


School  Systems 

Yearly  Gains 

10  to  11 

11  to  12 

12  to  13 

Hibbing                                    -           -     

2.32 

1.35 

1.41 

2.16 

.76 

.72 

.11 

1.39 
1.49 
1.64 
1.07 
1.36 
.93 
.31 

2.17 

Arkansas  City 

1.31 

Salina.-            _                         .         _     

.53 

Loixisville.  ...     ^         _--,.- 

.38 

Madison  County,  9-month  schools 

.80 

Louisiana..  ...         ...       .     

1.10 

Madison  County,  6-month  schools. . 

.05 

Total --       .  --  

8.83 

8.19 

6.34 

The  variations  in  amount  of  yearly  gain  are  as  great  as  they  are  in 
addition  and  subtraction.  The  greatest  gain  seems  to  be  between 
ages  10  and  11  in  this  case,  while  in  both  addition  and  subtraction  the 
greatest  gain  seems  to  come  between  ages  11  and  12.  The  smallest 
gain  appears  between  ages  12  and  13. 

The  conclusions  in  regard  to  multiplication  are  the  same  as  those  for 
addition  (p.  38)  and  subtraction  (p.  44). 


Section  4.     Division 
The  data  presented  in  division  are  from  the  same  sources  as  those 
for  addition,  subtraction  and  multiplication,  and  the  same  method  of 
treatment  has  been  followed. 


50         Study  of  Achievement  in  Country  and  Town  Schools 

Table  XXVIII  gives  the  facts  in  regard  to  division  in  the  6-month 
schools  of  Madison  County. 

TABLE  XXVIII 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 
Division  Rights  in  the  6-Month  White  Schools  of  Madison  County,  Ky. 


SCOBES 

XI 

X2 

0 

1 

2 

3 

4 

5 

6 

7 

8 

X9 

XIO 

XI 1 

in 

10 
6 
3 

2 

17 
10 
6 
3 

98 
83 
78 
70 

7 
15 
16 
16 

4 
1 
9 

8 

1 

5 

7 
5 

2 
2 
6 
1 

11 

12 

1 
4 

i 

1 

1 

2 

2 
4 
11 

2 

4 

2 

Total 


139 
126 
138 
123 


P.  E. true 

Median 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

.43 

.03 

.78 

0.07 

.35 

Mil— M10= 

.13 

.028 

11 

.56 

.04 

.94 

.18 

.38 

M12-M11  = 

.20 

.053 

12 

.76 

.09 

2.05 

.32 

.86 

M13— M12= 

.04 

.078 

13 

.80 

.10 

2.15 

.36 

.89 

M13— M10= 

.37 

.072 

In  these  schools  the  median  ability  in  division  of  each  of  the  age- 
groups  from  ages  10  to  13  inclusive  is  between  0  and  1.  For  the  ages  10 
and  11  the  75  percentiles  are  in  the  same  interval.  It  seems  that  in 
division,  as  in  multiplication,  the  majority  of  the  children  under  14 
years  of  age  in  the  Madison  County  6-month  schools  are  unable  to 
v^ork  correctly  any  of  the  examples  given  in  the  Courtis  Standard 
Research  Tests  in  Arithmetic  Series  B  for  division. 

The  total  gain  in  ability  to  divide  during  the  three-year  period  from 
ages  10  to  13  inclusive  is  from  .43,  the  median  for  the  10-year-old  chil- 
dren, to  .80,  the  median  for  the  13-year-old  children,  a  difference  of  .37. 
The  P.E.  of  this  difference  is  .072 — about  20  per  cent  of  the  gain. 
This  gain  is  very  small  for  so  long  a  period  of  time  at  the  age  w^hen 
material  progress  is  being  made  in  this  ability  in  other  school  systems. 

As  w^ould  be  expected  where  the  total  improvement  is  so  small,  the 
yearly  gains  are  very  small  and  uneven.  From  ages  10  to  11  the  gain 
is  .13;  from  ages  11  to  12  it  is  .20;  and  from  ages  12  to  13  it  is  .04. 
The  P.E.  of  the  gain  from  ages  12  to  13  is  .072,  which  is  almost  twice 
as  much  as  the  gain.  This  means  that  the  gain  in  this  year  is  almost 
negligible. 

Table  XXIX  gives  the  facts  in  regard  to  division  in  the  Madison 
County  9-month  schools. 


Achievement  Measured  bv  Courtis  Arithmetic  Tests 


51 


TABLE  XXIX 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 
Division  Rights  in  the  9-Month  White  Schools  of  Madison  County,  Ky. 


Scores 

Age 

Total 

XI 

q 

X2 
Ifi 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

X9 

XIO 

Xll 

10 

fin 

fi 

S 

5 

q 

4 

3 

1 

1 

1 

1 

1 

124 

11 

1 

q 

4fi 

6 

11 

3 

7 

2 

2 

2 

4 

1 

1 

1 

96 

12 

3 

1 

45 

13 

q 

10 

13 

11 

8 

8 

9 

1 

1 

2 

1 

1 

129 

13 

5 

3 

17 

15 

8 

11 

7 

6 

6 

3 

3 

3 

1 

1 

8 

1 

1 

99 

P.  E. true 

• 

Median 

—obtained 

75  per- 

(     25  per 

Q 

P.E. 

median 

centile 

eentile 

10 

.61 

.12 

2.37 

.11 

1.13 

Mil— M10=  .21 

.122 

11 

.82 

.16 

2.90 

.30 

1.30 

M12— Mll  =  1.45 

.190 

12 

2.27 

.21 

5.31 

.63 

2.34 

M13— M12=  .86 

.264 

13 

3.13 

.33 

6.37 

.98 

2.69 

M13— M10  =  2.52 

.210 

In  these  schools  the  25  percentile  of  each  of  the  age-groups  from  ages 
10  to  13  inclusive  falls  between  0  and  1,  and  the  medians  for  the  10- 
and  11-year-old  groups  each  fall  in  the  same  interval.  A  much  larger 
proportion  of  the  children  reported  are  able  to  work  some  of  the  ex- 
amples correctly  than  is  the  case  in  the  6-month  schools. 

The  total  gain  from  ages  10  to  13  inclusive  in  this  case  is  2.52  as 
against  .37  in  the  case  of  the  6-month  schools  in  the  same  county.  The 
P.E.  of  the  gain  for  the  9-month  schools  is  .21,  about  8.5  per  cent  of  the 
gain.  The  probable  actual  deviation  of  the  true  measure  of  gain  from 
the  measure  of  gain  given  is  almost  three  times  as  great  as  the  like 
probable  deviation  in  the  case  of  the  6-month  schools,  but  the  gain  in 
the  case  of  the  9-month  schools  is  so  much  greater  that  proportion- 
ately the  probable  deviation  is  smaller. 

As  in  the  6-month  schools,  so  in  these,  the  yearly  gains  are  unequal. 
From  ages  10  to  11  the  gain  is  .21 ;  from  ages  11  to  12  it  is  1.45 ;  and 
from  ages  12  to  13  it  is  .86.  The  gain  for  each  year  after  the  first  is 
much  greater  than  the  total  gain  in  the  6-month  schools  for  the  entire 
three-year  period. 

Tables  XXX  to  XXXIV  inclusive  give  comparative  data  from  other 
school  systems  in  regard  to  division.  In  the  following  summary  the 
total  gain  in  ability  to  divide  during  the  three-year  period  from  ages  10 
to  13  inclusive  is  given  for  each  of  the  systems  studied,  and  also  the 
median  ability  of  the  13-year-old  children  in  the  respective  systems. 
The  schools  are  listed  in  the  order  of  the  amount  of  improvement 
made. 

In  this  table  it  is  interesting  to  note  that  the  ranking  in  order  of 
amount  of  total  gain  corresponds  exactly  to  ranking  in  order  of  the 


52  Study  of  Achievement  in  Country  and  Town  Schools 


TABLE  XXX 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Division  Rights  in  Certain  White  Schools  of  Louisville,  Ky. 


Age 

Scores 

XI 

10 

5 

X2 

16 
10 
5 

X3 

43 
16 
10 
5 

0 

30 
23 
16 
11 

1 

24 
12 
12 
9 

2 

31 
16 
15 
13 

3 

24 
23 
18 
16 

4 

32 

28 
22 
13 

5 

21 
25 

22 
21 

6 

20 

>2 
23 
34 

7 

13 
20 

27 
23 

8 

9 

18 
27 
30 

9 

11 

19 
23 
25 

10 

3 
21 
23 
26 

11 

3 
12 
10 
25 

12 

4 
12 

17 
18 

13 

2 
9 
11 
13 

14 

"7 
12 
6 

15 

1 

3 
9 
12 

16 

17 

18 

19 

20 

21 

22 

23 

24 

X9 

10 

11 

3 
3 
6 

2 
6 
2 

1 
4 

1 
3 
2 

1 

1 

"26 

12 

13 

Total 


297 
308 
319 
336 


Median 

P.  E. true 

— obtained 

median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

11 

12 
13 

2.82 
5.84 
7.61 
8.76 

.19 

.24 
.23 
.21 

5.60 
9.68 
10.83 
12.05 

.17 
2.68 
4.17 

5.80 

2.71 
3.50 
3.33 
3.12 

M11-M10=3.02 
M12-M11  =  1.77 
M13— M12  =  1.15 
M13— M10=5.94 

.192 
.204 
.191 
.176 

TABLE  XXXI 
Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 


Division  Rights 

IN 

Certain  White  Schools 

IN 

Louisiana 

Scores 

A?p 

Total 

XI 

X2 

X3 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

X9 

XIO 

XI 1 

10 

24 
14 

7 

43 
24 
14 

59 
43 
24 

106 
90 
103 

16 

27 
32 

17 

19 
31 

9 
16 
22 

4 
16 
23 

4 
9 
13 

2 
7 

8 

7 

1 
3 

8 

1 

3 
7 

286 

11 

1 

1 

2 

2 

1 

1 

1 

282 

12 

1 

1 

1 

305 

13 

7 

14 

75 

37 

18 

15 

26 

22 

13 

10 

12 

6 

4 

3 

---- 

1 

16 

1 

1 

281 

P.  E. true 

Median 

— obtained 

75  per- 

25 per- 

Q 

P.E. 

median 

centile 

centile 

10 

.16 

.02 

.83 

0.00 

.33 

Mil— M10=  .50 

.060 

11 

.66 

.09 

2.70 

0.00 

1.35 

M12— Mll=  .48 

.092 

12 

1.14 

.12 

3.80 

.30 

1.75 

M13— M12=1.27 

.138 

13 

2.41 

.19 

5.85 

.65 

2.60 

M13— M10=2.25 

.120 

TABLE  XXXII 
Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 


D 

[VI 

SION 

Rights 

IN 

Arkansas  City 

Scores 

Age 

Total 

XI 

X2 

X3 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

X9 

10 

16 
8 
4 
1 

49 
16 
8 
4 

60 
49 
16 
8 

86 
81 
82 
42 

43 
38 
45 
29 

22 
10 
37 
25 

1 

1 
2 

9       7 
6       9 
9     19 
3     19 

2 

9 

11 

25 

1 

1 

10 

8 

295 

11 

6 
15 
23 

5 
12 
15 

7 
6 
5 

2 
9 
10 

257 

1? 

"h 

.... 

1 
3 

294 

13 

.... 

1 

1 

248 

P.  E.  true 

Medis 

n 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q   • 

P.E. 

10 

.26 

.04 

1.23 

0.00 

.61 

Mil— M10=  .42 

.053 

11 

.68 

.08 

2.07 

0.00 

1.03 

M12— Mll  =  1.14 

.102 

12 

1.82 

.14 

4.50 

.55 

1.97 

M13— M12=1.83 

.150 

13 

3.85 

.20 

6.43 

1.24 

2.59 

M13— M10=3.39 

.121 

Achievement  Measured  by  Courtis  Arithmetic  Tests 


53 


TABLE  XXXIII 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 
Division  Rights  in  Salina,  Kan. 


Scores 

Ape 

1 

XI 

16 

X2 
21 

X3 
47 

0 

48 

1 
41 

2 
39 

3 

27 

4 

28 

5 

21 

6 
21 

7 
9 

8 
12 

9 
2 

10 

11 

9 

12 

1 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

X9 

XIO 

10 

11 

3 
3 

16 
3 

21 
16 

36 
22 

21 
18 

29 

28 

37 
25 

17 
32 

29 
33 

16 
29 

16 
25 

25 

28 

1 
9 

0 

21 

4 

8 

4 
10 

0 

2 
2 

i 

2 
2 

- 

- 

- 

- 

-- 

2 

12 

?. 

13 

.... 

3 

3 

11 

17 

20 

27 

25 

29 

31 

14 

20 

11 

18 

14 

8 

10 

' 

2 

-- 

1 

2 

-- 

5 

2 

Total 


335 
297 
322 
275 


Median 


1.86 
3.60 
5.45 


P.  E. true 

— obtained 

median 


75  per- 
centile 


4.43 
6.85 
8.26 
9.56 


25  per- 
centile 


0.00 
.95 


2.21 
2.95 
2.80 
3.01 


Mil— M10  =  1.74 
M12— M11  =  1.S5 
M13— M12=1.35 
M13— M10=4.96 


P.  E. 


.158 
.176 
.176 
.166 


TABLE  XXXIV 

Age  Distribution,  10  to  13  Inclusive,  of  Courtis  Series  B  Arithmetic  Tests 

Division  Rights  in  Hibbing,  Minn. 


Scores 

Age 

Total 

X2 

X3 

0 

1 

2 

3 

4 

5 

6 

7  8 

9 

10 

11  1 

2  13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

X9 

XIO 

10 

16 

35 
16 

98 
60 

11 

22 
10 

14 
21 

■m 

11 
16 
12 

17 
13 

11 
15 
19 

12  1 

13  1 
IS  1 

1  4 
3  11 
3  14 

4 
10 
16 

5 
12 
13 

1 
7 
4  1 

5  2 
9  1 
3  3 

i 

3 

1 
5 

258 

11 

1 
3 

1 

'? 

1 

243 

1^ 

1 

1 

1 

4 

229 

13 

14 

10 

4 

4 

11 

8 

9  1 

3  12 

9 

10 

5  1 

0  8 

6 

2 

1 

2 

1 

2 

1 

... 

32 

4 

178 

P.  E. true 

Median 

— obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

10 

.79 

.17 

4.50 

.13 

2.18 

Mil— M10=2.36 

.172 

11 

3.15 

.27 

7.48 

.74 

3.37 

M12— Mll=2.82 

.220 

12 

5.97 

.27 

9.73 

2.96 

3.38 

M13— M12  =  3.47 

.327 

13 

9.44 

.45 

15.12 

5.18 

4.92 

M13— M10=8.65 

.172 

size  of  the  median  for  the  13-year-old  children.  This  is  not  true  in 
the  case  of  addition,  subtraction,  or  multiplication,  though  in  each  case 
there  is  a  marked  similarity  in  the  ranking. 


School  Systems 


Total  gain 


10  to  13 
inclusive 


Medians 


13-year-old 
children 


Hibbing 

Louisville 

Salina 

Arkansas  City 

Madison  County,  9-month  schools 
Louisiana 

Madison  County,  6-month  schools 


8.65 
5.94 
4.96 
3.39 
2.52 
2.25 
.37 


9.44 
8.76 
6.80 
3.65 
3.13 
2.41 
.80 


54         Study  of  Achievement  in  Country  and  Town  Schools 

The  following  table  shows  the  yearly  gain  in  ability  to  divide  in  each 
of  the  systems  studied : 


School  Systems 


Hibbing 

Louisville 

Salina 

Arkansas  City 

Madison  County,  9-month  schools 
Louisiana 

Madison  County,  6-month  schools 

Total 


Yearly  Gains 


10  to  11 


2.36 
3.02 
1.74 
.42 
.21 
.50 
.13 


.38 


11  to  12 


2.82 
1.77 
1.85 
1.14 
1.45 
.48 
.20 


9.71 


12  to  13 


3.47 
1.15 
1.35 
1.83 

.86 
1.27 

.04 


9.97 


The  variations  in  amount  of  yearly  gain  in  the  different  systems  is 
as  great  as  it  is  in  addition,  subtraction  and  multiplication.  The 
greatest  gain  seems  to  be  between  ages  12  and  13,  but  the  gain  from 
ages  11  to  12  is  almost  as  great.  The  gain  from  ages  10  to  11  is  some- 
what less.  It  seems  that  division  is  taught  when  the  children  are  a  lit- 
tle older  than  when  addition,  subtraction  and  multiplication  are  taught. 


CONCLUSIONS 

1.  The  difference  in  performance  in  arithmetic,  as  measured  by  the 
Courtis  Standard  Research  Tests  in  Arithmetic,  can  be  obtained  for 
school  children  of  different  ages. 

2.  Since  the  fundamental  processes  measured  by  this  test  are  largely, 
if  not  solely,  imparted  by  school  training,  this  difference  is  a  reliable 
measure  of  school  efficiency. 

3.  Since  the  improvement  measured  by  this  test  is  stated  in  terms  of 
examples  solved  in  a  given  time  rather  than  in  terms  of  difficulty  for 
the  children,  the  differences  obtained  must  be  considered  in  connec- 
tion with  the  number  of  examples  solved  by  the  groups  of  children  of 
different  ages. 

4.  The  differences  obtained  may  be  compared  for  two  systems  of 
schools,  even  though  the  testing  was  done  at  different  times  in  the 
respective  systems. 

5.  The  differences  obtained  are  valid,  even  though  there  are  con- 
stant errors  in  the  giving  of  the  tests,  such  as  might  be  caused  by  hav- 
ing the  tests  given  by  the  teachers. 


Achievement  Measured  by  Courtis  Arithmetic  Tests  55 

6.  Material  gain  may  be  made  in  these  fundamental  processes  of 
arithmetic  during  any  part  or  all  of  the  age  period  from  10  to  13  in- 
clusive. 

7.  The  results  in  the  6-month  schools  of  Madison  County,  Kentucky, 
are  uniformly  poorer  than  in  any  of  the  other  systems  studied. 


CHAPTER  V 

ACHIEVEMENT  AS  MEASURED  BY  THE  THORNDIKE  SILENT 
READING  SCALE  ALPHA  2 


The  Thomdike  Silent  Reading  Scale  Alpha  2  was  used  to  measure 
reading  in  the  schools  of  Madison  County  at  the  same  time  that  the 
tests  were  given  in  Language  and  Arithmetic.  This  scale  is  designed 
to  be  used  as  a  group  test,  and  the  directions  for  scoring  are  given  on 
the  basis  of  groups  of  pupils  such  as  would  be  found  in  one  room  of  a 
city  school  system.  In  country  schools  such  groups  do  not  exist,  and 
therefore  individual  scores  were  assigned  each  pupil,  on  the  basis  of 
tables  prepared  by  Dr.  Truman  Lee  Kelley.^ 

Using  the  individual  scores  assigned  on  the  basis  of  these  tables,  the 
remaining  problems  involved  in  finding  the  differences  in  performance 
in  reading  of  different  age-groups  are  practically  the  same  as  in  the 
work  with  the  Trabue  Language  Scale  and  the  Courtis  Standard  Re- 
search Tests  in  Arithmetic.  Distributions  for  the  respective  age- 
groups  are  completed  on  the  same  assumptions,  and  the  same  age- 
groups  are  used  throughout.  Scores  used  are  in  terms  of  difficulty  as 
assigned  by  Thorndike. 

Table  XXXV  gives  the  facts  in  regard  to  reading  in  the  Madison 
County  6-month  schools.  The  table  reads,  there  are  estimated  to  be 
8  children  10  years  old  in  the  first  grade  (XI)  whose  scores  in  read- 
ing are  unknown,  10  children  10  years  of  age  with  scores  unknown 
are  estimated  to  be  in  the  second  grade  (X2),  1  child  10  years  old 
made  a  score  of  2.0,  5  made  a  score  of  2.2,  3  a  score  of  2.6,  3  a  score 
of  2.9,  2  a  score  of  3.2,  etc. 

The  total  gain  in  ability  to  read  for  the  three-year  period  from  ages 
10  to  13  inclusive  is  from  4.50  to  5.26,  a  difference  of  .76.  The  P.E.  of 
this  difference  is  .09,  or  about  12  per  cent  of  the  total.  This  gain  is 
very  small  for  a  three-year  period,  and  the  P.E.  of  the  gain  is  relatively 
quite  large. 

The  improvement  from  year  to  year  is  very  uneven.  From  ages  10 
to  11  it  is  .03 ;  from  ages  11  to  12  it  is  .59;  and  from  ages  12  to  13  it  is 
.14.     The  results  indicate  rather  indefinite  work  in  reading. 


''  Kelley,  T.  L. :  "Thorndike's  Reading  Scale  Alpha  2  Adapted  to  Individual 
Testing,"  Teachers  College  Record,  XVIII:  253#.  (May,  1917). 

56 


Ace  Distribution.  10  to  13  Inclusive,  of  Thornd: 


TABLE  XXXV 
Silent  Reading  Scale  Alpha  2  Scores  : 


6-MoNTH  White  Schools  of  Madison  County,  Ky. 


Age 

Sco™ 

XI 

1 

^ 

- 

» 

5 

- 

'A 

i! 

1 

- 

i? 

2.9  3.0 

"i 
"i 

3.2 

2 

3.3 

~6 
5 
6 

> 

3.4 

3.5 

3.6 

i 
2 

" 

- 

3.8 

-° 

1 

;;: 

i 

2 

"i 

10 

^^ 

1 

3 

10 
10 

1 

10 

8 

7 
8 

"2 

-. 

-, 

^ 

" 

3 
4 

!l« 

6.0 

6.1 

6.2 

6.3  6.4 

6.5 

8.8 

a.; 

— 

6.9 

— 

LI 

— 

" 

LI 

Li 

^ 

LI 

X9 

XIO 

Xil 

1 

"1 

7 

il 

i 

"\ 

2 

..' 

-i 

l' 

' 

"i 

,• 

A8. 

ToUl 

M..i„ 

—obtained 

aS 

ceoUle 

Q 

P.E. 

i 

117 

i 

:i 

b'.23 

li 

:i 

Mll-M10=  .03 
M12-M11-  .59 
M13-M12.  .14 
M13-M10-  .76 

:o9 

Age  Distribution,  10  to  13  I 


TABLE  XXXVI 
Thorndike  Silent  Reading  Scale  Alpha  2  Sci 


;  9-Month  White  Schools  of  Madison  Countv,  Ky. 


tr' 

Sco.^ 

XI 

X2 

t 

1 

" 

LI 

2.6 

2.6 

". 

2.8 

5 

3.0 

3.1 

L: 

2 

-. 

-, 

3.6 

" 

- 

- 

-2 

-> 

L! 

Li 

Li 

i 

1.8 

'i 

3 

! 

1 

"-I 

3 

I 

^ 

1 

6 

2     2 
2     4 

1 

1 

1 

~ 

« 

T] 

3 

O 

3 

1 

^ 

1 

7.1 

1 

7.2 

7.3 

7.4 

7.5 

Li 

7.7 

- 

Li 

Li 

Li 

Li 

Li 

Li 

ii 

Li 

Li 

X9 

XIO 

\11 

1 

2 

12 

] 

1 

... 

1 

1 

1 

' 

' 

- 

= 



P  E  true 

Age 

ToUil 

Mtdian 

—obtained 
median 

ooDtilo 

eenUle 

Q 

P.E. 

10 

109 

4  55 

15 

5.51 

2.98 

1.26 

Mil— M10= 

75 

.14 

83 

6.45 

.93 

M13-M10- 

.90 

.12 

Age 


TABLE  XXXVII 
Age  Distribution,  10  to  13  Inclusive,  of  Thorndike  Silent  Reading  Scale  Alpha  2  Scores  op  Certain  White  Schools  in  Louisville,  Ky. 


Am 

SconES 

XI 
~10 

X2 

1 

0 

2.2 

2.3 

- 

" 

« 

iZ 

L? 

^ 

3.0 

- 

- 

« 

- 

- 

!_» 

-, 

- 

-. 

L° 

^ 

).2 

1 

' 

1 

" 

1 

^ 

( 
( 

8 
2 
2 

3 

! 

5.3 

1 

1 

" 

5.7 

~S 

I 

— 

i 

"> 

6J 

61 

^ 

13 

25 

O 

17 

-° 

IS 

1 
10 

,; 

" 

'] 

7.7 

7.8 

7.9 

8_0 

SA 

'jI 

8.3 

8.4 

8.6 

« 

X9 

XIO 

xu 

1 

11 

..' 

-1 

■i 

iS 

1 

1 

^ 

-3 

"i 

'^ 

J 

j 

' 





Age 

ToUl 

MkUjw 

P.li.tru. 

-obtained 

medijui 

centile 

25  per- 
centile 

Q 

P.E. 

10 

203 

5.09 
6.03 
6.45 

!08 
.07 
.0) 

7:3* 

l.Ol- 
4.86 
5.46 
6.37 

2.02 
.90 

M13— Ml6=i;81 

1 

lated  OD  the  assumption  that  the  scores  of  childrea  reported 
under  captions  XI,  X2  and  X3  are  distributed  cvenV  be- 

TABLE  XXXVIII 
Age  Distribution,  10  to  U  Inclusi\e.  of  Thorndike  Silent  Reading  Scale  Alpha  2  Scores  of  Hamilton  Township,  N.  J. 


Ak 

PCORIM 

_ 

XI 

X2 

0 

" 

" 

" 

" 

" 

" 

2J 

2J 

3.0 

3.1 

3.2 

— 

3.4 

" 

1 

". 

^ 

3^ 

« 

'i 

" 

\ 

z 

i 

1 

^ 

1 

1 

5.0 

1( 

5.2 

\ 

1 

-, 

5.6 
\ 

^ 

i 

7 

12 
7 
5 

^ 

'1 

5 

6 

8 

'S 

13 

8 

~, 

11 

^ 

^ 

^ 

n 

7.5 

7.6 

" 

7.8 

7.9 

8.0 

8.1 

8.2 

8.3 

8.4 

8.5 

M 

IZ 

8.8 

8.9 

« 

i:! 

9^ 

X9 

.-1 

1 

\ 

i 

-4 

2 

1 

^ 

^ 

-..' 

' 

' 

' 

' 

' 

'- 

Age 

Total 

Median 

P.E.tr.. 
median 

een^le' 

centile 

Q 

P.E. 

•No 

e  thai  the  rale  ii 

ot  charted  Irom  9. 

! 

?si 

6:77 

1 

6.04 

7:30 

yi 

;i 

Mll-MlO-  .72 
M12-M11-  .34 
M13-M12-  .52 
M13-M10.1.58 

:oi 

.05 
.05 

.09.6. 

TABLE  XXXIX 


Age  Distribution 

10 

TC 

13  I 

NC 

US 

VE 

0 

Thc 

RN 

DIK 

E 

Silent  Readin 

G  Scale  Alpha  2  Scores 

FO 

R  Am 

TE 

M, 

N 

\ 

Ale 

Sconm 

XI 

X2 

61 

1. 

" 

- 

- 

- 

2.6 

2.7 

2.8 

3 

3,0 

L! 

3.3 

— 

« 

1 

3.7 

» 

» 

!:.» 

4.2 

4.3 

4.4 

ij 

^ 

1 

4.8 

-: 

1 

i-» 

9 

'1 

1 

7 

1 

5.7 

8 

5.8 

1 

6.0 

1 

13 

6.3 

5 

" 

1 

6.8 

6 

■'8 

-] 

7.2 

"2 

"i 

-2 

- 

-' 

" 

7J 

L» 

O 

?d 

8.2 

^ 

8^ 

!i 

" 

" 

— 

O 

O 

X9 

V\ 

1 

; 

1 

"•i 

1 

1 

1 

6 

I 

2 

< 

■"= 

1 

' 

' 

- 

' 

Aee 

TO., 

M.*a 

—obtained 
median 

75  per- 
centile 

25  per- 
centile 

Q 

P.E. 

11 

255 
193 

3.70 
5.37 
6.99 
6.55 

!08 
.09 
.08 

6:87 
7.21 

4153 
5.29 

':L' 

Mll-M10=1.67 
M12-M11=  .62 
M13-M12.  .56 

1 

the  aaaumption  that  the  ecoroa  of  children  reportwi  under 
captions  XI.  X2  and  X3  are  diatributed  even&  between  0 

Achievement  Measured  by  Thorndike  Reading  Scale  57 

Table  XXXVI  gives  the  facts  in  regard  to  reading  in  the  9-month 
schools  of  Madison  County. 

The  total  gain  for  the  three-year  period  in  this  case  is  from  4.55, 
the  median  ability  of  the  10-year-old  children,  to  6.45,  the  median 
ability  of  the  13-year-old  children,  a  difference  of  1.90.  This  gain  is 
just  2.5  times  as  great  as  that  made  in  the  6-month  schools  of  the 
same  county.  The  median  abilities  of  the  10-year-old  children  are 
about  alike.  The  comparison  of  amount  of  gain  in  the  two  cases  is 
valid,  since  the  scores  given  are  in  terms  of  difificulty  for  the  children. 
It  must  be  remembered,  however,  that  there  is  no  proof  that  the  gain 
in  each  case  can  be  attributed  solely  to  school  work.  It  is  possible 
that  influences  outside  of  the  school  contribute  materially  to  the  re- 
sult. The  conclusion  can  only  be  that  school  influence  on  reading  and 
other  possible  influence  on  reading  accomplish  between  them  2.5  times 
as  much  in  places  having  a  9-month  school  term  as  do  the  same  in- 
fluences in  places  having  a  6-month  school  term. 

The  P.E.  of  the  gain  in  the  9-month  schools  (1.90)  is  .12,  about 
7  per  cent  of  the  gain.  The  probable  actual  deviation  of  the  true  dif- 
ference from  the  obtained  difference  in  these  schools  is  a  little  larger 
than  the  like  deviation  in  the  6-month  schools,  but  in  proportion  to  the 
gains  made  in  the  respective  schools  the  deviation  is  less  in  the  9-month 
schools. 

The  yearly  gains  are  much  more  nearly  uniform  than  in  the  6-month 
schools.  From  ages  10  to  11  the  gain  is  .75;  from  ages  11  to  12  it  is 
.56;  and  from  ages  12  to  13  it  is  .59. 

Tables  XXXVII  to  XXXIX  inclusive  give  comparative  data  in  re- 
gard to  reading  from  certain  other  school  systems.  The  data  from 
Louisville  are  based  upon  tests  given  by  the  Psychological  Laboratory 
of  the  Louisville  Board  of  Education.  Data  for  Hamilton  Town- 
ship, New  Jersey,  were  collected  by  the  Psychology  Department  of 
the  Trenton  State  Normal  School.  The  data  from  Amsterdam,  New 
York,  were  collected  by  the  Department  of  Educational  Administra- 
tion of  Teachers  College,  Columbia  University. 

In  the  following  summary  the  total  improvement  in  silent  reading  dur- 
ing the  three-year  period  from  ages  10  to  13  inclusive  is  given  for  each 
of  the  school  systems  studied,  and  also  the  median  ability  for  the  re- 
spective groups  of  13-year-old  children.  The  schools  are  listed  in  the 
order  of  the  amount  of  improvement  made. 


58  Study  of  Achievement  in  Country  and  Town  Schools 


Total  gain 

Medians 

School  Systems 

10  to  13 
inclusive 

13-year-old 
children 

Amsterdam          - _..     

2.85 
1.90 
1.81 
1.58 
.76 

6.55 

Madison  County,  9-month  schools _-          _     

6.45 

Louisville -     --           -     .- 

6.90 

Hamilton  Township _._ _. 

6.77 

Madison  County,  6-month  schools  . 

5.25 

The  ranking  in  order  of  amount  of  improvement  for  the  three-year 
period  from  ages  10  to  13  inclusive  does  not  correspond  exactly  with 
the  ranking  in  order  of  abiHty  of  13-year-old  children.  As  has  been 
pointed  out  in  the  case  of  language  and  arithmetic,  the  medians  for 
13-year-old  children  may  be  affected  by  constant  errors  in  any  of  the 
respective  systems,  such  as  a  tendency  to  overrun  the  time  allowance, 
a  little  greater  leniency  in  scoring  papers  in  one  place  than  in  another 
either  by  the  teachers  or  by  the  examiner,  in  giving  directions,  etc. 
Such  errors  are  compensating  when  the  difference  between  the  medians 
for  two  ages  is  used  as  a  measure,  since  these  errors  would  be  constant 
for  any  given  place  and  time  for  pupils  of  the  different  ages.  In  view 
of  this,  it  is  probable  that  the  ranking  in  order  of  total  gain  in  the  above 
table  is  the  more  significant  ranking. 

The  amount  of  gain  in  the  respective  systems  is  directly  comparable, 
since  the  scale  used  is  expressed  in  terms  of  units  of  difficulty  for  the 
children.  We  can  say  that  the  results  in  Amsterdam  for  the  three- 
year  period  from  10  to  13  inclusive  are  about  four  times  as  good  as 
are  the  results  in  the  Madison  County  6-month  schools,  and  about 
twice  as  good  as  the  results  in  Hamilton  Township.  However,  not 
all  of  the  improvement  noted  is  known  to  be  the  result  of  school  pro- 
cedure. A  good  share  of  the  gain  in  ability  to  read  silently  may  be 
due  to  forces  outside  of  the  school,  such  as  library  facilities,  home  in- 
fluence, newspapers,  etc.  Indeed,  it  is  sometimes  charged  that  school 
work  in  reading  stresses  oral  work  too  much.^  The  conclusion  from 
the  above  table  is  therefore  limited  to  the  statement  that  the  sum  of 
school  influence  in  reading  and  outside  influences  in  reading  is  about 
four  times  as  great  in  Amsterdam  as  in  the  Madison  County  6-month 
schools  for  the  equal  period  of  time  from  ages  10  to  13,  If  equality 
of  outside  influences  making  for  improvement  in  silent  reading  might 
be  assumed  for  the  different  systems  studied,  there  would  be  left  the 
single  variable  element  in  the  school  work  on  silent  reading.     It  does 


For  an  example  of  this  see  Klapper,  Teaching  Children  to  Read. 


Achievement  Measured  by  Thorndike  Reading  Scale 


59 


not  seem  probable,  however,  that  influences  other  than  those  of  the 
school  which  make  for  improvement  in  silent  reading  are  equal  in 
cases  such  as  Amsterdam,  New  York,  and  the  smaller  schools  of  Mad- 
ison County,  Kentucky. 

The  following  summary  shows  the  gain  for  each  age  period  of  a 
year  in  the  systems  studied : 


School  Systems 

Yearly  Gains 

10  to  11 

11  to  12 

12  to  13 

ATn<^terdam 

1.67 
.75 

.94 
.72 
.03 

.62 
.56 
.42 
.34 
.59 

.56 

Madison  County,  9-month  schools 

Louisville_        .     

.59 
.45 

Hamilton  Township 

.52 

Madison  County,  6-month  schools    

.14 

Total ...           .  . 

4.11 

2.53 

2.26 

The  variations  in  the  amount  of  yearly  gain  are  large,  as  is  the  case 
in  language  and  arithmetic.  The  greatest  gain  seems  to  be  from  ages 
10  to  11,  and  each  year  after  this  shows  less  gain  than  the  preceding 
year.  It  appears  that  greater  gain  is  made  by  younger  children  than 
by  older  ones  within  the  limits  of  the  age-groups  studied. 


CONCLUSIONS 

1.  The  difference  in  ability  in  silent  reading,  as  measured  by  the 
Thorndike  Silent  Reading  Scale  Alpha  2,  can  be  obtained  for  children 
of  different  ages. 

2.  Since  the  function  measured  by  this  scale  may  be  improved  by 
influences  outside  of  the  school,  as  well  as  by  school  training,  this  dif- 
ference cannot  be  considered  as  a  wholly  reliable  measure  of  school 
efficiency  in  teaching  silent  reading. 

3.  This  difference  does  give  a  reliable  measure  of  the  improvement 
in  silent  reading  due  to  all  causes  during  the  three-year  period  from 
ages  10  to  13  inclusive. 

4.  Since  the  improvement  measured  by  this  scale  is  stated  in  terms 
of  difficulty  for  the  children,  the  differences  obtained  in  the  respective 
systems  studied  may  be  compared  directly. 

5.  The  differences  obtained  may  be  compared  for  two  systems  of 
schools,  even  though  the  testing  was  done  at  different  times  in  the  re- 
spective systems. 


60  Study  of  Achievement  in  Country  and  Tozvn  Schools 

6.  The  differences  obtained  are  valid,  even  though  there  may  be 
constant  errors  in  the  giving  of  the  tests,  such  as  might  be  caused  by 
having  the  tests  given  by  the  teachers. 

7.  Greater  gain  in  silent  reading  seems  to  be  made  by  the  younger 
children  within  the  age  limits  studied  (ages  10  to  13  inclusive). 

8.  Material  gain  in  silent  reading  may  be  made  during  any  part  or  all 
of  the  period  from  ages  10  to  13  inclusive. 

9.  The  results  in  the  Madison  County  6-month  schools  are  much 
poorer  than  in  any  other  system  studied. 

10.  The  results  in  the  Madison  County  9-month  schools  compare 
favorably  with  those  in  the  other  systems  studied. 


CHAPTER  VI 
SUMMARY  AND  CONCLUSIONS 

This  study  was  undertaken  with  four  specific  objects  in  mind. 
These  objects  are  set  forth  in  Chapter  II,  and  are  stated  as  follows : 

First :  To  show  that  the  difference  in  performance  in  school  sub- 
jects of  children  of  different  ages  can  be  obtained. 

Second :  To  show  that  this  difference  is  a  measure  of  school  effi- 
ciency which  may  be  used  to  measure  schools  or  school  systems. 

Third :  To  apply  this  measure  to  a  system  of  country  schools. 

Fourth :  To  compare  the  results  in  this  country  school  system  with 
the  results  in  certain  city  school  systems. 

The  results  of  the  study  are  considered  in  the  light  of  these  aims. 
Sections  1,  2,  3  and  4  of  this  chapter  deal  respectively  with  the  pur- 
poses stated. 

Section  1 

The  purpose  as  stated  is  "to  show  that  the  difference  in  perform- 
ance in  school  subjects  of  children  of  different  ages  can  be  obtained." 

With  the  tests  used  such  differences  have  been  obtained  for  chil- 
dren from  10  to  13  years  of  age  inclusive.  As  the  work  progressed, 
certain  difficulties  became  apparent  which  seem  to  justify  the  following 
statements : 

The  tests  to  be  used  in  obtaining  age  differences  in  performance 
must  be  of  such  a  nature  that  identical  tests  can  be  given  in  identical 
manner  to  all  of  the  grades  tested.  Such  a  spelling  scale  as  that  de- 
vised by  Ayres  could  not  give  age  differences  because  the  12-year-old 
child  in  the  third  grade  would  have  a  score  on  a  test  different  from 
the  test  used  for  the  12-year-old  child  in  the  sixth  grade.  The  results 
for  children  of  like  age,  but  in  different  grades,  would  be  in  terms  that 
could  not  be  directly  compared. 

The  tests  should  be  given  in  as  many  as  possible  of  the  grades  of 
the  elementary  school.  The  tabulations  in  this  study  include  results 
for  grades  3  to  8  inclusive  and  in  some  cases  for  grades  4  to  8.  With 
results  from  children  in  these  grades  it  was  found  necessary  to  esti- 
mate the  number  of  children  in  the  lower  grades  of  the  respective 
ages  studied,  and  it  seemed  unwise  to  attempt  to  find  medians  for 

61 


62         Study  of  Achievement  in  Country  and  Town  Schools 

groups  of  children  under  10  years  of  age  because  of  the  Hmited  num- 
ber of  children  of  the  lower  ages  tested.  If  the  tests  could  have  been 
given  in  grade  2,  it  would  have  been  possible  to  calculate  medians  for 
children  under  10,  and  the  necessity  of  calculating  the  probable  num- 
ber of  10-to- 11 -year-old  children  in  grade  2  would  have  been  avoided, 
and  scores  could  have  been  assigned  them. 

Full  age-grade  tables  of  all  the  children  in  all  the  grades  of  the 
systems  studied  should  be  prepared.  Such  tables  give  a  very  desirable 
check  on  the  number  of  children  tested,  and  furnish  a  basis  for  esti- 
mation of  the  number  of  children  of  any  given  age  in  grades  not  tested. 

Tests  used  should  be  such  as  will  test  the  ability  of  the  children  in 
the  lower  grades  as  well  as  the  ability  of  those  in  the  higher  grades. 
The  work  with  Courtis  Standard  Research  Tests  in  Arithmetic  showed 
that  these  tests  do  not  measure  the  ability  of  lower  grade  children, 
since  a  great  many  children  were  unable  to  work  correctly  even  one 
of  the  examples  given.  A  test  that  includes  problems  less  difficult  than 
those  of  this  series  would  be  desirable. 

Tests  used  must  be  individual  tests  rather  than  group  tests ;  at  least 
it  must  be  possible  to  assign  individual  scores  on  the  basis  of  the  tests 
given.  This  is  necessary  in  order  that  the  individual  scores  of  chil- 
dren of  any  given  age  may  be  taken  from  the  different  grades  in  which 
these  children  are  tested  and  thrown  into  a  single  distribution  on  an 
age  basis. 

For  work  in  country  schools  there  is  an  added  need  for  individual 
tests  rather  than  group  tests,  since  groups  of  children  of  like  age  or 
grade  in  any  given  country  school  are  likely  to  be  small. 

The  above  statements  may  be  summarized  as  a  set  of  directions  for 
the  guidance  of  those  giving  tests  which  are  to  be  tabulated  on  an  age 
basis.     The  concise  directions  are  as  follows : 

1.  Select  tests  that  are  identical  for  all  the  grades  to  be  tested. 

2.  Test  as  many  of  the  grades  as  possible. 

3.  Make  full  age-grade  tables  of  all  the  children  in  all  the  grades. 

4.  Select  tests  that  measure  the  ability  of  all  the  children. 

5.  Use  individual  rather  than  group  tests. 

Section  2 

The  second  purpose  of  this  study  as  stated  is  "to  show  that  this  dif- 
ference is  a  measure  of  school  efficiency  which  may  be  used  to  meas- 
ure schools  or  school  systems." 

In  so  far  as  the  tests  used  measure  functions  affected  solely,  or  even 


Summary  and  Conclusions  63 

largely,  by  school  training,  the  difference  in  performance  of  children 
of  different  ages  seems  to  furnish  a  measure  of  school  efficiency.  In 
the  case  of  the  Trabue  Language  Scale  B  the  function  measured  has 
not  been  shown  to  be  fundamentally  one  dependent  on  school  training. 
In  the  case  of  the  Courtis  Standard  Research  Tests  in  Arithmetic 
Series  B  it  seems  that  the  function  measured  is  to  a  very  large  degree 
at  least  one  dependent  on  school  training;  therefore  in  this  case  the 
difference  obtained  is  one  that  is  chiefly  the  direct  result  of  the  school 
training  received  by  the  children  and  of  elimination,  and  for  that  rea- 
son may  be  considered  a  measure  of  the  effectiveness  of  that  training 
and  of  elimination.  In  the  case  of  the  Thorndike  Silent  Reading  Scale 
Alpha  2  the  function  measured  is  one  which  is  greatly  affected  by 
school  training,  but  which  may  also  be  greatly  affected  by  influences 
outside  of  the  school. 

Even  though  the  function  measured  be  one  which  is  affected  by  in- 
fluences other  than  school  training,  it  may  be  argued  that  the  work 
of  the  school  should  so  supplement  other  influences  brought  to  bear 
upon  the  children  as  to  secure  for  them  reasonable  development  of 
the  function  considered.  If  this  conception  of  the  work  of  the  school 
is  accepted,  the  difference  between  performance  of  children  of  differ- 
ent ages  seems  a  sound  measure  of  the  degree  to  which  the  school  has 
succeeded  in  its  effort  to  secure  the  desired  development. 

In  any  case  in  which  the  difference  in  performance  of  children  of 
different  ages  is  considered  as  measuring  some  function  other  than 
one  dependent  on  school  training  for  its  improvement,  the  difficulty 
lies  in  the  nature  of  the  test  rather  than  in  the  fact  that  the  age-differ- 
ences are  used.  The  same  criticism  would  apply  to  the  same  meas- 
urement if  grade  standards  were  used. 

There  are  a  few  advantages  that  the  use  of  age-differences  as  a 
measure  of  school  efficiency  seems  to  have  over  the  use  of  grade 
standards.  One  of  these  is  that  the  testing  may  be  done  at  any  con- 
venient time  in  the  school  year,  with  the  possible  exception  of  the  first 
three  or  four  weeks  of  the  school  term.  This  is  due  to  the  fact  that 
the  birthdays  of  any  age-group  of  children,  say  the  10-year-olds,  are 
distributed  throughout  the  year  in  the  same  way  as  are  the  birthdays 
of  any  other  age-group,  say  the  13-year-olds.  This  means  that  the  loss 
of  children  from  the  group  because  they  reach  a  higher  age  will  be 
compensated  by  the  accretion  of  other  children  from  the  next  lower 
age-group.  Moreover,  this  loss  and  accretion  continues  throughout 
the  school  year  and  for  each  age-group,  so  that  the  difference  between 


64  Study  of  Achievement  in  Country  and  Tozvn  Schools 

any  two  age-groups  is  a  constant  quantity.  During  the  first  few  weeks 
of  school  there  may  be  a  slightly  uneven  loss  in  school  ability  due  to 
the  vacation  period,  since  it  has  never  been  shown  that  the  retaining 
power  of  children  of  different  ages  is  the  same.  After  school  is  once 
well  under  way  this  uneven  loss  is  overcome,  and  the  testing  may  be 
done  at  any  convenient  time. 

Another  advantage  in  the  use  of  age-differences  as  a  measure 
of  school  efficiency  lies  in  the  fact  that  errors  such  as  those  caused  by 
having  the  tests  given  by  the  teachers  are  compensated,  since  such  er- 
rors are  identical  for  children  of  all  ages. 

A  further  advantage  in  the  use  of  age-differences  lies  in  the  fact 
that  the  effects  of  poor  grading  or  great  retardation  are  considered  in 
the  measurement  of  improvement.  The  necessity  of  correcting  grade 
results  for  retardation  is  avoided,  since  the  score  of  the  retarded  child 
of  any  given  age  has  entered  into  the  measurement  of  that  age-group. 

The  advantages  mentioned  above  are  of  particular  significance  for 
work  in  country  schools.  The  difficulties  involved  in  giving  tests 
where  the  schools  are  scattered,  the  grading  poor,  and  the  groups  of 
children  frequently  very  small,  make  it  especially  desirable  to  give 
tests  in  these  schools  at  the  most  convenient  time  of  the  year  and  to 
have  the  tests  given  by  the  teacher. 

Section  3 

The  third  purpose  of  this  study  as  stated  is  "to  apply  this  measure 
to  a  system  of  country  schools." 

This  purpose  has  been  accomplished  and  the  results  given  in  the 
treatment  of  the  respective  tests. 

Section  4 

The  fourth  purpose  of  this  study  as  stated  is  "to  compare  the  re- 
sults in  this  country  school  system  with  the  results  in  certain  city 
school  systems." 

The  Madison  County  6-month  schools  have  been  compared  through- 
out this  study  with  the  schools  in  the  same  county  having  a  9-month 
school  term.  In  addition  to  this  comparison,  the  results  of  the  Trabue 
Language  Scale  B  have  been  compared  with  results  from  Louisville, 
Kentucky;  Paterson,  New  Jersey;  and  St.  Paul,  Minnesota.  As  has 
already  been  pointed  out,  this  comparison  concerns  the  results  of 
school  training  and  also  other  influences.  The  9-month  schools  in 
Madison  County  made  a  gain  in  the  ability  to  complete  sentences  53 


Summary  and  Conclusions  65 

per  cent  greater  than  the  gain  made  over  the  same  three-year  period 
in  the  6-month  schools.  None  of  the  systems  studied  made  a  gain  so 
great  as  that  of  the  Madison  County  9-month  schools,  and  all  of  them 
except  St,  Paul  made  gains  greater  than  did  the  Madison  County 
6-month  schools.  St.  Paul  made  practically  the  same  gain  as  did  these 
schools. 

If  the  comparison  is  made  on  the  basis  of  the  final  ability  attained 
by  the  children  (medians  for  13-year-olds),  the  Madison  County  6- 
month  schools  are  poorer  than  any  of  the  others  studied.  Louisville 
13-year-old  children  possess  50  per  cent  greater  ability  to  complete 
sentences  than  do  those  in  the  smaller  schools  of  Madison  County. 
,The  children  of  the  same  age  in  the  9-month  schools  possess  25  per 
cent  greater  ability  than  do  the  children  of  the  6-month  schools.  The 
10-year-old  children  in  Louisville  possess  greater  ability  to  complete 
sentences  than  do  the  13-year-old  children  in  the  6-month  Madison 
County  schools,  and  so  do  the  12-year-old  children  in  the  9-month 
schools,  the  11-year-olds  in  Paterson  and  the  10-year-olds  in  St.  Paul. 

Whichever  basis  of  comparison  is  used,  the  Madison  County  6- 
month  schools  are  at  the  bottom.  If  the  age  achievement  is  used 
as  the  basis  of  comparison,  the  Madison  County  9-month  schools  are 
only  kept  from  the  bottom  by  the  presence  of  the  6-month  schools 
among  the  systems  compared. 

In  comparing  the  work  in  arithmetic  it  must  be  remembered  that 
the  results  are  in  terms  of  examples  worked  correctly  in  a  given  length 
of  time,  and  that  it  cannot  be  assumed  that  it  is  twice  as  difficult  to 
add  8  examples  as  it  is  to  add  4  in  the  same  time.  Bearing  in  mind 
this  caution,  it  seems,  on  the  basis  of  the  results  obtained,  that  while 
the  pupil  in  the  Madison  County  6-month  schools  is  increasing  his 
ability  to  add  to  such  an  extent  that  he  can  add  one  more  example  in 
the  time  allowed,  the  pupil  in  the  Madison  County  9-month  schools  is 
increasing  his  ability  to  add  by  1.6  examples,  the  pupil  in  Louisiana  by 
2.2,  the  one  in  Arkansas  City  by  2.7,  the  one  in  Salina  by  3.0,  the  one  in 
Louisville  by  3.4,  and  the  one  in  Hibbing  by  5.7  examples. 

In  subtraction  the  situation  is  much  the  same.  While  the  pupil  in 
the  Madison  County  6-month  schools  is  improving  his  ability  to  sub- 
tract by  1  example,  the  one  in  the  9-month  schools  of  the  same  county 
is  improving  his  ability  by  3.1,  the  one  in  Salina  by  3.2,  the  one  in 
Louisiana  by  3.3,  the  one  in  Arkansas  City  by  4.2,  the  one  in  Louis- 
ville by  4.8,  and  the  one  in  Hibbing  by  5.8  examples. 


66         Study  of  Achievement  in  Country  and  Town  Schools 

While  the  pupil  in  the  6-month  schools  of  Madison  County  is  im- 
proving his  ability  to  multiply  to  such  an  extent  that  he  can  multiply 
one  more  example  in  the  time  allowed,  the  pupil  in  Louisiana  improves 
his  ability  so  that  he  can  multiply  5.8  more  examples  in  the  time  al- 
lowed, the  pupil  in  the  Madison  County  9-month  schools  improves  by 
6.2  examples,  the  one  in  Louisville  by  7.7,  the  one  in  Salina  by  7.8, 
the  one  in  Arkansas  City  by  8.8,  and  the  one  in  Hibbing  by  12.5  ex- 
amples. 

In  division  the  situation  is  even  worse.  While  an  improvement  of 
one  example  is  being  made  by  the  pupil  in  the  Madison  County  6- 
month  schools,  there  is  an  improvement  of  6.1  by  the  pupil  in  the 
Louisiana  schools,  of  6.8  in  the  Madison  County  9-month  schools,  of 
9.1  in  Arkansas  City,  of  13.4  in  Salina,  of  16.1  in  Louisville,  and  of 
23.4  in  Hibbing. 

If  the  comparison  be  put  on  the  basis  of  achievement  of  13-year-old 
children,  the  situation  in  the  Madison  County  6-month  schools  does 
not  seem  to  be  much  better.  The  median  13-year-old  child  in  these 
schools  can  neither  add,  subtract,  nor  multiply  as  well  as  the  median 
10-year-old  in  Hibbing,  and  he  can  barely  divide  as  well.  The  Madi- 
son County  9-month  schools  do  better  on  this  basis,  but  the  median  for 
the  13-year-old  children  is  below  the  median  for  the  11-year-old  chil- 
dren in  Hibbing  in  addition,  subtraction,  multiplication  and  division. 

The  comparison  of  the  results  of  the  Thorndike  Silent  Reading 
Tests  shows  conditions  which  are  not  quite  so  disastrous  for  the 
Madison  County  6-month  schools  in  that  the  differences  are  not  so 
great.  On  the  basis  of  improvement,  while  the  pupil  in  the  Madison 
County  6-month  schools  is  improving  his  ability  to  read  by  one  step 
on  the  Thorndike  scale,  the  pupil  in  Hamilton  Township  improves  2.1 
steps,  the  one  in  Louisville  2.4,  in  the  Madison  County  9-month  schools 
2.5,  and  in  Amsterdam  3.7  steps.  On  the  basis  of  age  achievement 
the  median  13-year-old  child  in  the  Madison  County  6-month  schools 
is  poorer  than  the  median  11-year-old  child  in  Hamilton  Township, 
Louisville,  and  Amsterdam,  and  almost  as  poor  as  the  median  11-year- 
old  child  in  the  Madison  County  9-month  schools. 

The  comparison  of  the  Madison  County  6-month  schools  with  the 
other  schools  tested  may  be  summed  up  in  the  statement  that  the  chil- 
dren in  these  schools  have  less  ability  along  every  line  tested  than  have 
the  children  of  the  same  ages  in  other  schools,  and  that  they  are  learn- 
ing more  slowly,  except  that  the  children  in  St.  Paul  are  improving  as 
slowly  as  they  do  in  language. 


Summary  and  Conclusions  67 

Final  Summary 

The  following  four  statements  seem  justified  concerning  the  four 
purposes  for  which  this  study  was  undertaken : 

First :  The  difference  in  performance  in  school  subjects  can  be  ob- 
tained for  children  of  different  ages. 

Second :  This  difference  is  a  measure  which  may  be  used  to  meas- 
ure schools  or  school  systems,  and  has  certain  advantages  for  this  pur- 
pose, especially  in  rural  schools. 

Third :  This  measure  has  been  applied  to  a  system  of  country 
schools. 

Fourth :  The  Madison  County  6-month  schools  compare  unfavor- 
ably with  all  of  the  other  schools  measured.  The  Madison  County 
9-month  schools  compare  more  favorably. 


APPENDIX 


For  the  convenience  of  any  who  may  wish  to  supplement  the  re- 
port made  in  Chapter  I  of  scientific  studies  on  the  results  of  instruc- 
tion in  rural  schools,  or  who  may  later  wish  to  bring  this  report  up  to 
date,  this  statement  of  the  educational  literature  investigated  is  made. 

As  a  first  step  in  searching  for  such  data  the  following  surveys  were 
studied.  In  each  case  the  tables  showing  the  results  were  investigated 
to  find  what  scores  might  be  included  from  rural  schools  in  the  com- 
parisons made. 

SURVEYS 

Connecticut  (counties). 


Akron,  Ohio. 

Alabama  (three  counties). 

Alabama.* 

Alton,  111. 

Amsterdam,  N.  Y. 

Anderson,  Ind. 

Arizona.* 

Ashland,  Ore. 

Atlanta,  Ga. 

Baltimore,  Md. 

Binghamton,  N.  Y. 

Blaine,  Wash. 

Bloommgton,  Ind. 

Boise,  Idaho. 

Boston,  Mass. 

Bridgeport,  Conn. 

Buffalo,  N.  Y. 

Brookline,  Mass. 


Butte,  Mont. 

Chicago,  111.  (Educational  Commission). 

Cincinnati,  Ohio. 

Cleveland,  Ohio. 

Cleveland,  Ohio.f 

Colorado. 

Cold  Springs,  N.  Y.  (Haldane  School).  Indiana  (Vocational). 

Colorado  (rural  schools).  Janesville,  Wis. 

Columbia,  S.  C.  Jefferson  County,  Ind.  (Vocational). 

Connecticut  (Educational  Commission).  Kansas  (high  schools). 


Dansville,  N.  Y.  (High  School). 

Dayton,  Ohio. 

Delaware.! 

Delaware  (School  Buildings). 

Denver,  Col. 

Detroit,  Mich.  (Recreational). 

Elyria,  Ohio.* 

Evansville,  Ind.  (Vocational). 

Framingham,  Mass. 

Gary,  Ind.* 

Gary,  Ind.J 

Georgia  (Counties). 

Grafton,  W.  Va. 

Grand  Junction,  Col. 

Grand  Rapids,  Mich. 

Great  Neck,  L.  I. 

Greene  County,  Ind. 

Greenwich,  Conn. 

Hammond,  Ind.  (Industrial). 

Harrisburg,  Pa. 

Herkimer,  N.  Y. 

Huron  County. 

Illinois  (State). 


*United  States  Bureau  of  Education. 
fRussell  Sage  Foundation. 
JGeneral  Education  Board. 


68 


Appendix 


69 


Lane  County,  Ore. 

Los  Angeles,  Cal. 

Leavenworth,  Kan. 

Louisville,  Ky. 

Maricopa  County,  Ga. 

Maryland  (State). J 

Memphis,  Tenn.* 

Minneapolis,  Minn.  (Vocational). 

Missouri   (Saline  County). 

Montclair,  N.  J. 

Nassau  County,  N.  Y. 

Newburgh,  N.  Y. 

New  Orleans,  La.  (Vocational). 

Newton,  Mass. 

New  York  City. 

North  Dakota.* 

Oakland,  Cal. 

Ogden,  Utah. 

Ohio. 

Oklahoma. 

Oklahoma  (county). 

Oswego  County,  N.  Y. 

Paducah,  Ky. 

Paterson,  N.  J. 

Port  Townsend,  Wash. 

Portland,  Ore. 

Reading,  Pa. 


Rochester,  Minn. 

Rockford,  111. 

St.  Louis,  Mo. 

St.  Paul,  Minn. 

Salt  Lake  City,  Utah. 

San  Antonio,  Texas. 

San  Francisco,  Cal. 

San  Mateo,  Cal. 

Saskatchewan,  Canada. 

Solvay,  N.  Y. 

South  Bend,  Ind. 

South  Dakota.* 

Stamford,  Conn. 

Syracuse,  N.  Y. 

Travis  County,  Texas. 

Utica,  N.  Y. 

Van  Wert,  Ohio. 

Vermont.f 

Virginia  (Educational Commission). 

Washington.* 

Waterbury,  Conn. 

Westchester,  N.  Y. 

Wilmington,  Del.* 

Windsor  County,  Vt. 

Wisconsin   (State). 

Winston-Salem,  N.  C. 

Wyoming.* 


The  next  step  in  the  search  for  data  bearing  on  the  objective  results 
of  instruction  in  rural  schools  was  a  study  of  A  Selected  Bibliography 
of  Certain  Phases  of  Educational  Measurements,  prepared  by  Edna 
Bryner  and  published  in  the  Seventeenth  Year  Book  of  the  National 
Society  for  the  Study  of  Education,  1918.  The  titles  listed  were 
examined,  and  whenever  there  seemed  any  possibility  that  the  article 
might  contain  any  data  concerning  country  schools  the  article  was  stud- 
ied. One  bulletin  by  E.  J.  Ashbaugh,  entitled  The  Arithmetical  Skill 
of  Iowa  School  Children,  University  of  Iowa  Extension  Bulletin,  No. 
24,  November,  1916,  was  not  found.  In  all,  twenty-eight  of  the  ref- 
erences were  examined,  and  of  these  five  were  found  to  contain  data. 

As  a  final  step  in  the  search  for  material  bearing  on  the  comparison 
of  country  and  city  schools  by  the  use  of  objective  standards,  a  study 
was  made  of  the  monthly  lists  of  current  educational  publications  pre- 


*United  States  Bureau  of  Education. 
fRussell  Sage  Foundation. 
JGeneral  Education  Board. 


70  Study  of  Achievement  in  Country  and  Town  Schools 

pared  by  the  United  States  Bureau  of  Education,  beginning  with  the 
list  for  June,  1917,  and  extending  through  the  list  for  October,  1920. 
In  this  study  every  title  and  subtitle  was  considered,  and  in  case 
there  seemed  a  possibility  that  objective  data  might  be  found,  the 
reference  was  investigated.  In  this  study  only  two  articles  which 
seemed  to  bear  in  any  way  on  this  topic  were  not  found.  These  refer- 
ences are:  (1)  Johnson,  W.  E.,  "Reading,  Writing,  Arithmetic  and 
Spelling  in  City  and  Town  Schools  of  South  Dakota  in  1917-1918," 
Bulletin  of  the  Northern  Normal  and  Industrial  School  at  Aberdeen, 
S.  D.,  Vol.  XII,  No.  2  (October,  1918) ;  and  (2)  Heckert,  J.  W., 
"The  Cleveland  Survey  Tests  in  Arithmetic  in  the  Miami  Valley," 
Elementary  School  Journal,  XVIII :  447-457. 


t^t^Livr^.E  LIBRARY  or 
L.  H.  PETERSON, 


WIL 


;'3r,AL  ^ISRARy  FACILITY 


A     000  506  847     3 


